## Upcoming Seminars

### 7th June 2023 - 10am BST

#### Guido Franchetti- The asymptotic structure of the hyperbolic 2-monopole moduli space

It is well known that, in contrast with the Euclidean case, the *L ^{2}* metric on the moduli space of hyperbolic monopoles is not well defined. It is certainly possible to define a moduli space metric by other means, and there are various proposals in the literature. However whether or not these proposed metrics have any relation with the adiabatic dynamics of hyperbolic monopoles is unclear. To better understand this point, in this talk I describe what the asymptotic behaviour of a metric capturing the dynamics of 2 hyperbolic monopoles should be. The result is derived making used of the point particle approximation and, in analogy with the Euclidean case, the resulting metric is a hyperbolic version of negative mass Taub-NUT. This talk is based on arXiv:2302.13792 in collaboration with Calum Ross.

## Previous Seminars

### 31st May 2023 - 10am BST

#### Tomáš Brauner - Chiral soliton lattice in quark matter under extreme conditions

Watch on YouTube.

The lightest hadrons observed in nature are pseudoscalar mesons: the pions. These can be viewed as quark-antiquark bound states and therefore have vanishing baryon number; they do not constitute matter in the usual sense. However, as proposed long ago by Skyrme, baryon number can emerge effectively as a topological charge, carried by topologically nontrivial pion field configurations. The formation of such solitons – the skyrmions – is associated with a characteristic energy scale, corresponding to the scale of the nucleon mass. In this talk, I will introduce a novel phase of quark matter where a topologically realized baryon number appears at low energies, provided a suitable external field is present. Indeed, I will show that in sufficiently strong magnetic fields, a one-dimensional soliton lattice carrying baryon number becomes the ground state of quantum chromodynamics. The basic theoretical description of this Chiral Soliton Lattice (CSL) phase is very well known, and relies on the mathematics of a simple pendulum. I will discuss to some extent the spectrum of fluctuations of the CSL state and the effect of these fluctuations on the phase diagram. In the last part of the talk, I will give an overview of related work on the realizations of the CSL phase in quark matter under a variety of external conditions.

### 24th May 2023 - 10am BST

#### Filipp Rybakov - Braids formed by skyrmion strings

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Magnetic skyrmions are vortex-like spin textures in two dimensions, while in the third dimension, they resemble strings or strands.

We will consider the solutions of the field theory model and experimental observations of how such strings intertwine and form statically stable skyrmion braids in chiral magnets such as B20 FeGe.

Based on Nat. Commun. 12, 5316 (2021).

### 17th May 2023 - 10am BST

#### Giacomo Santoni - Aspects of the Electroweak Skyrmion

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The Electroweak Skyrmion (EWS) is a non-topological soliton of the electroweak sector of the Standard Model that arises when a stabilizing dimension-8 operator is included. We present a numerical solution of the equations of motion, which provides the mass, the radius and the magnetic moment of the classical EWS. We also discuss the quantization of the light degrees of freedom (spin, isospin and breather) and show that the EWS is a boson. From the classical solution, we infer the interaction potential between two well-separated EWSs and the fermionic number arising from the coupling between the soliton fields and the Standard Model leptons. We discuss the quantum stability of the EWS and roughly estimate its decay rate. Based on arXiv:2303.07164.

### 22nd March 2023 - 10am GMT

#### Matthew Edmonds - Dark quantum droplets and solitary waves in beyond-mean-field Bose-Einstein condensate mixtures

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Quantum liquid-like states of matter have been realised in an ongoing series of experiments with ultracold Bose gases. These peculiar states of matter have been studied experimentally in dipolar and binary quantum gases, arising due to the balance between the van der Waals interactions and the Lee-Huang-Yang (LHY) correction, originating from quantum fluctuations. Using a combination of analytical and numerical methods we identify the specific criteria for the existence of dark solitons in beyond-mean-field binary condensates, revealing how these excitations exist for both repulsive and attractive interactions, the latter leading to dark quantum droplets with properties intermediate between a dark soliton and a quantum droplet. The phenomenology of the these excitations are explored within the full parameter space of the model, revealing the novel spatial profile of the excitation that differs significantly from the Zakharov-Shabat (ZS) soliton; leading to a negative effective mass that is enhanced in the presence of the quantum fluctuations. Finally the dynamics of pairs of the excitations are explored, showing non-integrable dynamics and dark soliton bound-states in the attractive regime.

### 15th March 2023 - 10am GMT

#### Kaushlendra Kumar - Exact gauge fields from anti-de Sitter space

Watch on YouTube.

In 1977 Lüscher found a class of SO(4)-symmetric SU(2) Yang--Mills solutions in Minkowski space,
which have been rederived 40 years later by employing the isometry S^{3} ≅ SU(2) and
conformally mapping SU(2)-equivariant solutions of the Yang--Mills equations on (two copies of)
de Sitter space dS_{4} ≅ ℝ × S^{3}.
Here we present the noncompact analog of this construction via AdS_{3} ≅ SU(1,1).
On (two copies of) anti-de Sitter space AdS_{4} ≅ ℝ × AdS_{3} we write down SU(1,1)-equivariant Yang--Mills solutions and conformally map them to ℝ^{(1,3)}.
This yields a two-parameter family of exact SU(1,1) Yang--Mills solutions on Minkowski space,
whose field strengths are essentially rational functions of Cartesian coordinates.
Gluing the two AdS copies happens on a dS_{3} hyperboloid in Minkowski space, and our Yang--Mills
configurations are singular on a two-dimensional hyperboloid dS_{3} ∩ ℝ^{(1,2)}.
This renders their action and the energy infinite, although the field strengths fall off fast
asymptotically except along the lightcone.
We also construct Abelian solutions, which share these properties but are less symmetric and of zero action.

### 8th March 2023 - 10am GMT

#### Jaime Mendizabal- A Construction of Monopole Moduli Spaces for Arbitrary Symmetry Breaking

Monopoles over Euclidean 3-space have been studied in great detail for the gauge group SU(2), where we know that they form moduli spaces which carry complete hyper-Kahler metrics. For higher gauge groups, however, there are still many open questions. In this talk, based on upcoming work, we will provide a construction of the moduli space of monopoles for arbitrary gauge group and symmetry breaking, which is purely differential-geometric, and provides a hyper-Kahler metric

### 1st March 2032, 1pm GMT

#### Tomasz Romańczukiewicz and Nick Manton - The Simplest Oscillon and its Sphaleron

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We have constructed a small-amplitude oscillon solution for a simple 1-d scalar field theory with cubic potential, using the Fodor et al. expansion. The theory also has an exact sphaleron solution, which can decay slowly, via a larger-amplitude oscillon. The sphaleron's two discrete linearised modes, the unstable mode and a vibrational mode, provide a useful truncation of the field theory, connecting the sphaleron and the oscillon. We show how these various approximations tie together.

### 22nd February 2023, 10am GMT

#### Ivan Smalyukh - Crystals and clusters of three-dimensional topological solitons in liquid crystals and magnets

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### 8th February 2023 - 10am GMT

#### Peter Gerlagh - Bogomolny solutions in non-axisymmetric chiral magnets

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We characterise skyrmions in Bogomolny models of chiral magnets without axisymetry. We show a duality between these Bogomolny models and the specific Bogomolny model wherein the so-called DMI tensor is rank one. The potential in these models have two separate minimums and corresponding stationary vacuums. Exact solutions with skyrmions are build around a domain wall which separates these vacuums. The domain walls themselves can be characterised by a position and an angle.

### 1st February 2023 - 10am GMT

#### Harry Braden - Curves and Monopoles: Old and New

The modern approach to integrable systems typically proceeds via a curve, the spectral curve, with the parameters of the curve encoding the actions of the system and the solutions of the integrable system being built from appropriate functions on the curve. I will describe some generic features of this approach, focussing particularly on the curve, and illustrate a number of new and old results. Throughout I will focus on BPS monopoles for the system of equations of interest though the results are more widely applicable.

### 14th December 2022, 10am GMT

#### Maxim Chernodub - Rotation with imaginary angular frequency in Yang-Mills theories: calorons, phase structure, and fractals

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We find an instanton (caloron) solution in the finite-temperature SU(2) gluon gas subjected to (imaginary, in Euclidean spacetime) rotation. We demonstrate that the imaginary rotation leads to the delocalization of its topological charge over fractionally charged constituents. Furthermore, we show that in the high-temperature limit, the rapidly-rotating caloron becomes a ``circulon'': a self-dual monopole (dyon) possessing a spatial toroidal core. We also present the results of first-principle numerical simulations of Euclidean SU(3) Yang-Mills plasma rotating with a high imaginary angular frequency and discuss fractal thermodynamics associated with imaginary rotation.

### 7th December 2022 - 10am GMT

#### Kai Shao - Vortices and cosmic strings in the Born-Infeld model

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The Born-Infeld theory has long been an important nonlinear model in electrodynamics. The model was introduced by Max Born and Leopold Infeld to overcome the issue of the infinite energy of electric point charge. This talk is focused on vortices and cosmic strings in the Born-Infeld theory. After a brief introduction to the classical Born-Infeld model, I will discuss a generalized Born-Infeld model and its BPS equations. I will present the existence of the solution with prescribed vortices to the system using the method from PDE. After that, I will discuss the cosmic string problem when the equations of motion of the Born-Infeld model are coupled with the Einstein equations. The cosmic strings are realized as static solutions with prescribed zeros to the coupled system. I will also discuss the proof of the existence of such solutions.

### 30th November 2022 - 10am GMT

#### Filip Blaschke - Mechanization of scalar fields in 1+1-dimensions - An agnostic approach to Collective Coordinate Models

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We present a general-purpose Collective Coordinate Model for scalar field dynamics in 1+1 dimensions that we dubb `mechanization'. The idea is to `chop up' a continuous field into *N* straight segments. The positions of joints and slopes of the segments become the collective coordinates in a family of effective mechanical theories.

We show that even such a simplistic `triangulation' of configuration space does capture all essential phenomena of field dynamics in the case of the ϕ^{4} model. We emphasize the benefits and drawbacks of our approach and point out future directions.

### 16th November 2022, 10am GMT

#### Pawel Klimas - Compact oscillons

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Compact oscillons are peculiar exact solutions in the signum Gordon model. Unperturbed, they live indefinitely without losing energy. They also play an important role as a mechanism of emission of energy from excited kinks in models with non-analytic (V-shaped) potentials where the mass threshold is formally infinite. The radiation spectrum in such models is dominated by oscillon-type compact packages. I will discuss these solutions and their interaction which involves a scattering problem considering oscillon-oscillon and oscillon-kink configurations.

### 9th November 2022, 4pm GMT

#### Fabrizio Canfora - Analytic techniques in the analysis of solitons in the low energy limit of QCD

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In this talk effective analytic techniques able to disclose relevant physical features of the non-perturbative configurations of the low energy limit of QCD will be introduced. In particular, it will be discussed how such framework allows to analyze explicitly transport properties of Baryonic tubes and layers. The electric and thermal conductivities as well as the shear viscosity of the known analytic hadronic non homogeneous condensates at finite Baryon density in the Skyrme model in (3+1) dimensions will be discussed. The qualitative agreement of the analytic formulas with the phenomenological data will be emphasized.

### 2nd November 2022, 10am GMT

#### Benjamin Bode - Stable knots and links in electromagnetic fields

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An electromagnetic field consists of two time-dependent vector fields on ℝ^{3}, namely the electric and the magnetic field, which together satisfy Maxwell's equations. Sets of closed flow lines of a vector field form a link. We show that for every link *L* there is an electromagnetic field, whose magnetic field has a set of closed flow lines ambient isotopic to *L* for all time, and whose time evolution is given by pushforwards by a family of diffeomorphisms.

The closed flow lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.

If time permits, I will also discuss similar stability results for nodal links (or vortex links) that are formed by the zeros of the fields.

### 26th October 2022 - 10am BST

#### Albert Samoilenka - Ground state fractal crystals

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Is it possible to have a fractal as a stable state of a classical field theory? Are uniform, wave-like states and solitons all there is to it? We propose a simple continuous-space-discrete-field model whose ground state is a crystal, where each unit cell is a fractal. Based on arXiv:2206.04343.

### 19th October 2022 - 10am BST

#### Claire Cisowski - Optical Skyrmions

We introduce a simple mathematical expression based on rational maps to construct ideal paraxial optical skyrmions fields including Neel-type and Bloch-type skyrmions, anti-skyrmions, bimerons and multi-skyrmions, including skyrmion lattices. We review the rules that fully polarized paraxial light fields must obey to be considered as optical skyrmions. This work provides guidelines for the experimental generation of general skyrmion fields, beyond conventional single skyrmion beams. This lays the foundation for the exploration of nucleation and annihilation mechanisms in multiskyrmions fields. Based on arXiv:2207.12741

### 12th October 2022 - 10am BST

#### Azadeh Mohammadi - Fermion mediated resonance in fermion-kink systems

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This talk will focus on fermions bound by kink structures. This subject has been considered several times in the literature. However, in many of these studies, the back reaction of the fermions on the kinks has been neglected or considered only in the static case. We included the back reaction of the fermion on the colliding kink-antikink. The fermion field generates a force, either attractive or repulsive, depending on the distribution of the fermion field on kink and antikink. We have shown that the collision and the consequent resonance windows could be highly affected by the presence of the fermion. In this talk, I will also present one of the most fascinating conclusions of our study, which was that the fermion could also mediate the energy exchange mechanism, generating resonance windows even for integrable sine-Gordon model.

### 28th September 2022 - 10am BST

#### Tigran Tchrakian - Chern-Simons (CS), Higgs--Chern-Simons (HCS) and Skyrme--Chern-Simons (SCS)

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After some standard definitions, certain examples of solitons in systems featuring Chern-Simons (CS) dynamics are quoted. Specifically, the unusual dependence of the mass on electric-charge and angular momentum are quoted in Abelian gauged 2+1 and 4+1 dimensional models including CS terms. (In the 2+1 dimensional case, also the "baryon number" can change.) Motivated by these results, it is proposed to find CS-like densities for systems in both odd and even dimensions, and all (allowed) gauge groups. The first of these are the Higgs-CS (HCS) densities which result from the dimensional descent of Chern-Pontryagin densities, and the second are the Skyrme-CS (SCS) densities that are extracted from the gauge deformed baryon number densities that are themselves defined in all dimensions and for all (allowed) gauge groups. It turns out that the SCS densities are useful for application in soliton construction, while the HCS find application in Chern-Simons gravities.

### Geometric Models of Nuclear Matter Conference

For more details, and a nicer table, go to the Conference Website.

To watch a recorded talk, just click on the talk title.

There are also posters!

### 1st July 2022 - 2pm BST

#### SIG X: Luiz Ferreira - A Quasi Self-Dual Skyrme Model

Watch on YouTube.

### 1st July 2022 - 10am BST

#### SIG X: Sven Bjarke Gudnason - Nineteen vortex equations and integrability

Watch on YouTube.

### 30th June 2022 - 2pm BST

#### SIG X: Chris Halcrow - Instanton-generated skyrmions for nuclear physics

Watch on YouTube.

### 30th June 2022 - 10am BST

#### SIG X: Patrick Dorey & Tom Romanczukiewicz - Collisions of weakly-bound kinks

Watch on YouTube.

### 29th June 2022 - 2.30pm BST

#### SIG X: Alberto Garcia Martin-Caro - Kaon condensation and strangeness in compact stars

Watch on YouTube.

### 29th June 2022 - 2pm BST

#### SIG X: Jorge Castelo - Universal relations for rotating boson stars

Watch on YouTube.

### 29th June 2022 - 10am BST

#### SIG X: Peter Forgacs & Lucacs Arpad - Q-balls: Something old and something new, with components one and two

Watch Peter's talk and Arpad's talk on Youtube.

### 28th June 2022 - 2pm BST

#### SIG X: Piotr Bizon - Soliton resolution conjecture

Watch on YouTube.

### 28th June 2022 - 10am BST

#### SIG X: Jarah Evslin - A Less Powerful Approach to Quantum Kinks

Watch on YouTube.

### 27th June 2022 - 2pm BST

#### SIG X: Zoltan Bajnok & Marton Lajer - Bootstrapping and measuring S-matrices and form factors

Watch Zoltan's talk and Marton's talk on Youtube.

### 27th June 2022 - 10am BST

#### SIG X: Nick Manton - Skyrmion Challenges from Nuclear Physics

Watch on YouTube.

### 24th June 2022 - 3pm BST

#### SIG X: Carlos Naya - Hunting 3D solitons in frustrated magnets

Watch on YouTube.

### 24th June 2022 - 10am BST

#### SIG X: Bruno Barton-Singer - Magnetic skyrmion stability

Watch on YouTube.

**Open problems:**

How are the 'zero tension domain wall' and 'diverging decay lengthscale methods of calculating elliptical instability' related?

Can we model the collapse instability?

Can we find lower-energy periodic groundstates of the chiral magnet than those found so far by using higher charge solutions/varying the lattice properly as well?

### 23rd June 2022 - 3pm BST

#### SIG X: Jose Queiruga - Domain wall strings

Watch on YouTube.

### 23rd June 2022 - 10am BST

#### SIG X: Martin Speight - Geometry of vortices on the sphere in the dissolving limit

Watch on YouTube.

### 22nd June 2022 - 3pm BST

#### SIG X: Yasha Shnir - Boson stars and hairy black holes

Watch on YouTube.

### 22nd June 2022 - 11am BST

#### SIG X: Paul Leask - Skyrmion crystals

Watch on YouTube.

### 22nd June 2022 - 10am BST

#### SIG X: Miguel Huidobro - Asymmetric nuclear EoS and kaon condensation in Skyrme neutron stars

Watch on YouTube.

**Open problems:**

Is it possible to construct a full EoS (from the crust to high densities) within the Skyrme model?

More nuclear physics observables are needed to constrain the values of the parameters, since NS observations are too not restrictive. A good try could be to fit the compression modulus.

Also the Coulomb energy seems important in the low density regime of the neutron star. Maybe we could be appear to describe the pasta phase structures with the Skyrme model.

### 21st June 2022 - 3pm BST

#### SIG X: Dominik Ciurla - Bose-Einstein condensate and a negative radiation pressure

Watch on YouTube.

### 21st June 2022 - 10am BST

#### SIG X: Andy Royston - Quantum Solitons: A Review of the Canonical Transformation Approach

Watch on YouTube.

### 20th June 2022 - 10am BST

#### SIG X: Andrzej Wereszczynski - Kink collisions: an overview

Watch on YouTube.

### 27th April 2022 - 10am BST

#### Nick Manton - Quantum Statistical Mechanics of Vortices

Watch on YouTube.

The classical statistical mechanics of BPS (Abelian Higgs) vortices was calculated exactly some time ago, assuming purely kinetic dynamics on moduli space. This talk discusses the quantised analogue, where the Hamiltonian is proportional to the Laplace--Beltrami operator on moduli space. The asymptotic partition function at high temperature combines the classical result and the first quantum correction, which depends on a curvature integral. The quantum correction can reverse the sign of the second viral coefficient.

### 6th April 2022 - 10am BST

#### Alberto Garcia Martin-Caro and Muigel Huidobro - Quantization and low density regime of Skyrme crystals.

Watch on YouTube.

The Skyrme crystals are periodic, infinitely extended solutions which can be used to describe isospin-symmetric infinite nuclear matter. However, isospin asymmetry must be taken into account for a more accurate description of matter inside neutron stars. In the first part of the talk we will present the results of including the symmetry energy effects via the canonical quantization of collective coordinates of the Skyrme crystals, which also allows us to constrain the parameters of the model with measurements from nuclear experiments. In the second part we will explain the problem of describing the crust of NS with Skyrme crystals, and how a new set of periodic solutions, combined with quantum corrections, can help to solve this problem. Besides, the existence of these new solutions points towards the presence of a transition between different solutions near the crystal energy minimum.

### 30th March 2022 - 10am BST

#### Emine Şeyma Kutluk - Adiabatic Solutions in General Relativity as Null Geodesics on the Space of Boundary Diffeomorphisms

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We use Manton approximation for general relativity on manifolds with spatial boundary; which results in a description of the slow-time dependent solutions as null geodesics on the space of boundary diffeomorphisms, with respect to a metric we prove to be composed solely of the boundary data. We show/conjecture how the solutions in the bulk space are fixed via the constraint equations of general relativity. Furthermore, we identify our resulting Lagrangian as a generalized version of the covariantized Lagrangian for continuum mechanics. We study the cases of 3+1 and 2+1 dimensions and show that for the solutions we propose, the -harder to untangle- Hamiltonian constraint becomes the real homogeneous Monge-Ampere equation in the special case of two spatial dimensions.

### 23rd March 2022 - 10am GMT

#### Prim Plansangkate - Quadric Ansatz for the mn-dKP Equation and related Einstein-Weyl Spaces

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We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation. For one of these generalisations, we study solutions which are constant on a central quadric. The quadric ansatz leads to a second order ODE which is equivalent to Painleve I or II for the dKP equation, but fails to pass the Painleve test in higher dimensions. The second generalisation of the dKP equation leads to a class of Einstein-Weyl structures in an arbitrary dimension, which is characterised by the existence of a parallel weighted vector field, together with further holonomy reduction. We obtain an explicit local form for a family of Einstein-Weyl spaces belonging to this class, and depending on one arbitrary function of one variable.

### 16th March 2022, 10am GMT.

#### Kaushlendra Kumar - Yang-Mills solutions on Minkowski space via non-compact coset spaces

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We compute solutions of Yang-Mills equation on Minkowski space by foliating different parts of it with non-compact coset spaces arising from the Lorentz group SO(1,3). The interior of the lightcone is foliated with hyperbolic space H^{3} which is isomorphic to SO(1,3)/SO(3), while the exterior of the lightcone isfoliated with de Sitter space dS_{3} which is isomorphic to SO(1,3)/SO(1,2). The equivariant reduction of the Yang-Mills system on these coset spaces yields a mechanical system with inverted potential admitting analytic solutions, including the "kink". We also present the energy-momentum tensor for these solutions.

### 9th March 2022, 10am GMT.

#### Calum Ross - Calorons and constituent monopoles

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Calorons are instantons on ℝ^{3}×S^{1}, e.g. instantons with a periodic direction. Depending on the size of the circle they can look like instantons on ℝ^{4} or monopoles on ℝ^{3}. The known examples, such as those due to Krann-van Baal and Lee-Lu, have an interpretation in terms of constituent monopoles. This picture can be formalised to give a construction of *SU*(2) calorons as a superposition of BPS monopoles and "rotated BPS" monopoles glued into a singular background. The singular background consists of Abelian Dirac monopoles with both positive and negative charges. I will sketch some of the basics about calorons and give an outline of this construction as well as how it can be generalised to *G* calorons, for *G* an arbitrary simple group. This is joint work with Lorenzo Foscolo.

### 2nd March 2022, 10am GMT.

#### Julien Garaud - Quartic bosonic metallic state and its topological properties

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Superconductivity is an ordered quantum state with a long-range coherence of pairs of electrons, the Cooper pairs, which leads to zero resistivity and diamagnetism. I will present the recent observations of a new resistive state, coined quartic bosonic metal, characterized by the absence of long-range order between Cooper pairs but with order between pairs of pairs.

Unlike the superconductors, which break the U(1) gauge symmetry, this state spontaneously breaks the (discrete) time-reversal symmetry, and exhibits unconventional magnetic properties. I will demonstrate that the quartic bosonic metal state can be effectively accounted for, by a Faddeev-Skyrme-like model for the four-fermion order parameter. Its spectrum of topological excitations is rich, as it hosts domain-walls, magnetic-flux-carrying skyrmions, and most likely hopfions.

### 23rd February 2022, 10am GMT.

#### Bruno Barton-Singer - Long-range magnetic soliton interactions and the elliptical instability

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The chiral magnet supports a range of solitons, such as the skyrmion (Q=-1) antiskyrmion (Q=+1) and skyrmionium (Q=0) solutions. When there is a magnetic field applied to the magnet at an arbitrary tilt, skyrmion and antiskyrmion solutions are known to still be stable. Only the interaction potential between two skyrmions in untilted field has been calculated explicitly up until now. Separately, the stability regions of these solitons have been numerically observed but not much explained.

In this talk I will discuss the interaction potential between skyrmions and antiskyrmions in tilted field and the interaction potential in untilted field between more novel configurations. Along the way I will also discuss how we can model the `elliptical instability' of magnetic solitons and thus approximate some boundaries in the phase diagram of the chiral magnet.

### 16th February 2022, 10am GMT.

#### Bjarke Gudnason and Chris Halcrow - A Smörgåsbord of Skyrmions

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We study static solutions of the standard Skyrme model with a pion mass. Using approximately 105 pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated solutions, we find 409 local energy minimizers (Skyrmions) of the model with baryon numbers 1 through 16, of which 385 are new. In particular, we find new solutions for baryon numbers 5, 8, 9, 10, 11, 12, 13, 14, 15, and 16. Our results for the number of solutions per baryon number suggest that this number could grow either polynomially or exponentially. We identify new families of solutions: sheets of Skyrmions in synchronized and antisynchronized hexagonal layers (which we call graphene); chains of 2- and 3-tori; chain-like solutions containing a hinge and many clustered Skyrmions. Contrary to common lore, only the *B*=12 global energy minimizer is made of alpha particles or some chunk of a cubic crystal, whereas the *B*=9,11,14,15 minimizers contain the *B*=7 icosahedrally symmetric Skyrmion as a component. The *B*=10,13,16 are symmetric graphene-like solutions. We find *B*=5 and *B*=8 minimizers with numerically indistinguishable energies. The *B*=8 candidates are the chain of two cubes, which is a chunk of the cubic Skyrme crystal and the fullerene-type ball found originally by the rational map approximation. The *B*=5 global minimizer is either the well-known *D*_{2d} symmetric fullerene or a new *C*_{2v} symmetric solution. Finally, our findings show a large number of solutions have no discrete symmetries or just one symmetry, contrary to the common lore that Skyrmions are highly symmetric configurations.

### 9th February 2022, 10am GMT.

#### Steven Cotterill - Predicting the stability of vortons

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In this talk I will be discussing the stability of loops of superconducting cosmic string, known as vortons, to non-axially symmetric perturbations. By calculating a few integrated quantities of straight string solutions we can accurately predict the stability properties of vortons, if they are large enough that the effects of curvature can be neglected. Using this analysis, we have predicted the existence of stable vortons and performed supporting 3D simulations by perturbing our constructed solutions.

### 8th December 2021, 10am GMT.

#### Paul Sutcliffe - Boundary metrics on soliton moduli spaces.

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The geodesic approximation to soliton dynamics is extended to situations in which the standard metric is infinite, by considering boundary metrics on soliton moduli spaces. Examples are presented, including a hyperbolic analogue of the Atiyah-Hitchin manifold, relevant to the scattering of a pair of hyperbolic monopoles.

### 24th November 2021, 10am GMT.

#### Alberto Alonso Izquierdo - Scattering between wobbling kinks

Watch on YouTube.

The kink-antikink scattering in the φ^{4}-model involves
fascinating properties. One of them is the presence of a fractal
structure embedded in the final versus initial velocity diagram. The
kink reflection processes included in this regime involve *n*-bounce
events where the kink and the antikink collide and bounce back a
finite number of times before escaping away. The excitation of the
shape modes of the colliding kinks makes that the subsequent
collisions in an *n*-bounce event involve the scattering between
wobbling kinks or wobblers. In this talk we shall discuss the
scattering between wobblers in the standard φ^{4} model in two
different scenarios, which give rise to constructive or destructive
interference between the shape modes at the collision.

### 17th November 2021, 10am GMT.

#### Jose Queiruga - Excitations of global vortices

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In this talk I will discuss the spectrum of linearized excitations of global vortices in 2+1 dimensions. After identifying the existence of localized excitation modes, the decay time scale of the first two will be compared with the results given by the numerical evolution of the full non-linear equations. I will show numerically how the interaction of vortices with an external source of radiation or other vortices can excite these modes dynamically. I will also explore the evolution of a network of vortices in an expanding (2+1) dimensional background, in particular, in a radiation dominated universe and analyze the excitation of the internal modes.

### 10th November 2021, 1pm GMT.

#### Uri Kol - Duality and Infrared Phenomena in Einstein's Gravity

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In this talk I will describe a phenomenon akin to Electric-Magnetic duality in Einstein's gravity. I will show that a new type of "magnetic" dual gravitational charges generate redundant symmetry transformations which are not part of the standard group of diffeomorphisms. The new gauge symmetry of the metric reveals, in turn, a wide class of IR phenomena including: monopole solutions, double copy structure of scattering amplitudes and more.

### 3rd November 2021, 1pm GMT.

#### Masaru Hongo - Instanton, inhomogeneous phase, and Nambu-Goldstone mode in chiral magnets

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The Dzyaloshinskii-Moriya (DM) interaction, described by a term proportional to the vector product of neighboring spins, is a specific interaction for spin systems to favor inhomogeneous order. In this talk, I will present some interesting analytic results for chiral magnets (or spin systems with the DM interaction) after demonstrating how we can implement the DM interaction into the O(3) nonlinear sigma model. By considering several types of the DM interaction, I will explain various instanton solutions [1] and the inhomogeneous ground states (helical and spiral phases) together with the energy spectrum of the Nambu-Goldstone modes [2].

Ref.

[1] M. Hongo, T. Fujimori, T. Misumi, M. Nitta, N. Sakai, Phys.Rev.B 101 (2020) 10, 104417

[2] M. Hongo, T. Fujimori, T. Misumi, M. Nitta, N. Sakai, Phys.Rev.B
104 (2021) 13, 134403

### 27th October 2021, 1pm BST.

#### Jan Albert - The Abrikosov vortex in curved space

Watch on YouTube.

It is known that when coupled to gravity, 't Hooft-Polyakov monopoles can hold a Schwarzschild black hole at their core, realizing a hairy magnetic black hole. In this talk we will try to construct a similar object with Abrikosov vortices. So we will study the Abrikosov vortex in curved space, first in the asymptotically flat case and later in AdS, discussing both singular and non-singular solutions. We will end with some comments on the interpretation of these objects in the context of AdS/CFT, touching on the story of the holographic superconductor.

### 13th October 2021, 10am BST.

#### Juan Carlos Criado - Electroweak skyrmions in the HEFT

Watch on YouTube.

We will see how skyrmions, topological solitons originally found in an effective theory for pions, may arise also in the electroweak sector, including a dynamical Higgs boson. A powerful tool for studying them, with applications in many other non-perturbative problems, are neural networks. We will discuss their use in computing the skyrmion solutions and the shape of the energy functional. This allows to find which effective operators can stabilize them. Finally, we will consider some phenomenological aspects of skyrmions: the collider signatures of their stabilizing operators, and their potential as Dark Matter candidates.

### 6th October 2021, 10am BST.

#### Kenji Fukushima - Deformation of Skyrmions under a magnetic field and the domain-wall formation

Watch on YouTube.

In a nuclear system with chiral symmetry and a magnetic field, SU(2) symmetry is explicitly broken down to U(1), and the baryon number winding should be changed accordingly. I will first discuss deformation of isolated baryons in a magnetic field and explain two interesting observations; the magnetic assisted confinement and the mass splitting between protons and neutrons by a topological term. I will next discuss the Skyrme Crystals under a magnetic field and show two solutions. One corresponds to deformed nuclear matter and the other to the uniform pionic domain wall. I will finally show the phase diagram as a function of the density and the magnetic field.

### SIG IX Schedule

This is a copy of the SIG IX schedule from the SIG website.

All times are European Central Summer Time (Brazil Standard time -5 (6 am/10 am), British Summer Time -1 (10 am/14 pm), China Standard Time + 6 (5 pm/9 pm) and Japan Standard Time + 7 (6 pm/10 pm).Recordings of the talks will appear on this webpage, as well as the official SIG page.

To join a seminar, enter the usual Solitons at Work Zoom room.

#### Monday 28th June

10.50: Welcome by Kasia Oles and Andrzej Wereszczynski

11.00: Wormholes and Solitons, Nick Manton [Watch].

15.00: Self-Duality: applications of Skyrme theory to nuclear matter, Luiz Ferreira [Watch].

#### Tuesday 29th June

11.00: Collective coordinate model of kink-antikink collisions in phi^4 theory by Kasia Oles, Tom Romanczukiewicz and Andrzej Wereszczynski [Watch].

15.00: Short talks:

- Yasha Shnir, "Spinning Q-balls and boson stars" [Watch].
- Carlos Naya, "Skyrmion tubes in liquid crystals" [Watch].
- Andy Royston, "Simulating magnetic monopole-defect dynamics" [Watch].
- Andreas Fring, "Degenerate and nonlocal soliton solutions from PT-symmetry" [Watch].
- Paul Leask, "The baby Skyrme crystal" [Watch].

#### Wednesday 30th June

11.00: Topological Defects in Multicomponent Ginzburg Landau Theory, Martin Speight [Watch].

15.00: The geometry of chiral skyrmion dynamics, Bernd Schroers [Watch].

#### Thursday 1st July

11.00: Skyrmions from instantons, Josh Cork, Chris Halcrow, Derek Harland and Tom Winyard [Watch].

15.00: Skyrme crystals - nuclear matter and neutron stars, Alberto Garcia Martin-Caro and Miguel Huidobro [Watch].

#### Friday 2nd July

11.00: Near-BPS (baby) Skyrmions as an approach to nuclear physics, Bjarke Gudnason [Watch].

15.00: Quantum corrections to the ANO vortex, Herbert Weigel [Watch].

16.30: Closing remarks by Nick Manton [Watch].

### 26th May 2021, 10am BST.

#### Calum Ross - Magnetic Impurities, Integrable Vortices and the Toda Equation

Watch on YouTube.

The five known integrable Abelian vortex equations are generalised to include magnetic impurities. Exploring this leads to a Tong-Wong type product group gauge theory of coupled vortices. For a suitable choice of charge matrix these coupled vortex equations reduce to either the integrable Toda equation or an opposite sign version. I will sketch this construction and highlight the integrable cases.

### 19th May 2021, 10am BST.

#### Daniel Jimenez - Exciting the kink

Watch on YouTube.

In many field theories, solitonic solutions admit localized excitations with unnaturally long lifetimes in their spectrum of perturbations. These bound states may play a significant role in the dynamics of solitons, and in particular, they could shed light on some aspects concerning the evolution of cosmic string networks. As a starting point, we investigate the properties of this type of excitations in the simple case of the (lambda phi^4) theory in 1+1 dimensions. This talk will be devoted to a detailed characterization of the shape mode perturbation of the kink solution. We study its decay rate and its level of excitation in Minkowski spacetime as well as in two cosmological settings: the formation of kinks in a phase transition and the interaction of the kink with a thermal bath.

### 12th May 2021, 10am BST.

#### Andreas Fring - Non-Hermitian gauge field theories and BPS limits

Watch on YouTube.

We present an overview of some key results obtained in a recent series devoted to non-Hermitian quantum field theories for which we systematically modify the underlying symmetries. Particular attention is placed on the interplay between the continuous symmetry group that we alter from global to local, from Abelian to non-Abelian, from rank one to generic rank N, and the discrete anti-linear modified CPT-symmetries. The presence of the latter guarantees the reality of the mass spectrum in a certain parameter regime. We investigate the extension of Goldstone's theorem and the Higgs mechanism, which we demonstrate to work in the conventional fashion in the CPT-symmetric regime, but which needs to be modified technically at the standard exceptional points of the mass spectrum and entirely fails at what we refer to as zero exceptional points as well as in the broken CPT-symmetric regime. In the full non-Hermitian non-Abelian gauge theory we identify the t'Hooft-Polyakov monopoles by means of a fourfold Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We investigate this limit further for other types of non-Hermitian field theories in 1+1 dimensions that possess complex super-exponential and inverse hyperbolic kink/anti-kink solutions and for 3+1 dimensional Skyrme models for which we find new types of complex solutions, that all have real energies due to the presence of different types of CPT-symmetries.

### 5th May 2021, 10am BST.

#### Sven Bjarke Gudnason - 1/2-BPS vortex strings in N=2 supersymmetric U(1)^{N} gauge theories

Watch on YouTube.

Strings in N=2 supersymmetric U(1)^{N} gauge theories with *N* hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomol'nyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in SU(2)_{R} space. We further prove for all cases, that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the SU(2)_{R} symmetry in the equations, after the constraint equations have been solved.

### 28th April 2021, 4pm BST.

#### Bob Decker - Kink-Antikink Initial Conditions and Interactions for Field Theories with Polynomial Tails

Watch on YouTube.

Field theories with polynomial tails, as in the case of the
φ^{8}, φ^{10}, and φ^{12} theories, present new challenges for
the computer simulation of interactions involving kinks and antikinks. In particular,
a naive sum ansatz of a single kink and antikink is shown to be an
inadequate choice on which to base initial conditions. The results contained
in a recent paper (and two preceding ones) in which the authors investigate such
simulations and methods for generating good initial conditions, will be presented.
The meaning of "good" in this context is one primary focus of the talk.
It is shown that constrained minimization processes are needed to distill the best possible
initial conditions from various ansatze. Some results of resonance windows
for these theories will also be discussed.

Phys. Rev. D 99, 016010 (2019), https://arxiv.org/abs/1810.03590

Phys. Rev. Lett. 122, 171601 (2019), https://arxiv.org/abs/1811.07872

Commun. Nonlinear Sci. Numer. Simulat. 97 (2021) 105748, https://arxiv.org/abs/2005.00154

### 21st April 2021, 4pm BST.

#### Noah Kent - Target skyrmions, topological stability, and hopfions in experimental chiral ferromagnetic systems

Watch on YouTube.

Topologically non-trivial structures in ferromagnetic systems have garnered significant interest in recent years due to their technological potential and interesting mathematical properties. In this talk I will discuss the experimental realization and identification of target skyrmions and hopfions in chiral ferromagnetic Ir/Co/Pt multilayer heterostructures. I will detail how micromagnetic energies are tuned in experimental chiral ferromagnetic systems, how these nanostructures are made with nanofabrication, and how they are identified using multiple types of x-ray magnetic circular dichroism microscopies.

Throughout this talk, I hope to identify some differences between topological theory and scientific experiment; for example in a real magnetic system the stability of topologically non-trivial structures is very important as topological transformations are possible at accessible energies due to the finite scale of the system and discrete nature of the magnetization.

Based on papers: https://aip.scitation.org/doi/10.1063/1.5099991, and https://www.nature.com/articles/s41467-021-21846-5

### 7th April 2021, 10am BST.

#### Andrzej Wereszczynski - (Collapse of) the vibrational moduli space and soliton dynamics

Watch on YouTube.

I will show that thin spectral walls (a long range intersoliton interaction due to a transition of the normal mode to the continuum spectrum) are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol'nyi-Prasad-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. I will also show that they can be found as points where the dynamical vibrational moduli space has singularities.

### 31st March 2021, 10am BST.

#### Gabriel Luchini - Towards hidden symmetries in gauge theories

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In this talk, we address and solve two long standing problems in non-abelian gauge theories. The first one is the construction of truly gauge invariant electric and magnetic charges that are dynamically conserved. The second one is the proof that the Wu-Yang monopole configuration can only be a consistent solution of pure SU(2) Yang-Mills theory if a point source, of a very definite form, is added to it. Those two results were made possible by an educated use of the integral Yang-Mills equations. We end by showing how such integral equations can be used to uncover hidden symmetries of the Yang-Mills theory on loop space.

### 24th March 2021, 10am GMT.

#### Jarah Evslin - Quantum Kink States

Watch on YouTube.

We introduce two (compatible) new methods for the treatment of quantum kinks. First, we present a simpler and faster alternative to collective coordinates in which the momentum operator is treated perturbatively. It is less powerful than collective coordinates, but well-suited to certain problems such as finding quantum kink states and mass corrections. Second, we note that if the kink sector Hamiltonian is defined by a unitary transformation on the defining regularized Hamiltonian, then it automatically has the same spectrum and no regulator matching condition need be imposed. This new definition solves a problem from the last century, when it was shown that the usual definition of the kink sector Hamiltonian leads to the wrong quantum kink mass if the theory is regulated with an energy cutoff. We then apply these two advances to calculate two-loop mass corrections to quantum kinks and to compute the corresponding quantum states at two loops. The ground state is treated, as well as states excited by normal modes.

### 17th March 2021, 10am GMT.

#### Avner Karasik - Skyrmions, one flavored baryons, and one current to rule them all

Watch on YouTube.

It has been proposed by Komargodski in arxiv.org/abs/1812.09253 that baryons in Nf=1 QCD can be described as singular solitons in the effective theory of the eta' meson. This construction raises the question of continuity between these solitons and the standard skyrmions. I will introduce corrections to the skyrmion current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The contribution to the charge from these corrections is non-trivial only for singular configurations as the Nf=1 baryons. This modified current gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. The desired corrections can be derived from the effective Lagrangian assuming specific interactions between pions and vector mesons.

Remarkably, these interactions coincide in the large N limit with the phenomenological principle of vector mesons dominance. This coincidence provides an experimental evidence for the construction of Nf=1 baryons, as well as a theoretical explanation to vector dominance.

### 10th March 2021, 10am GMT.

#### Yuki Amari - Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

Watch on YouTube.

We will discuss an SU(3) generalization of magnetic skyrmions. Magnetic skyrmions are two-dimensional topological solitons, in most cases, stabilized by the Dzyaloshinskii-Moriya (DM) interaction. For the SU(3) generalization, we first derive an SU(3) counterpart of the DM interaction from a spin system, as well as the CP^2 nonlinear sigma model simultaneously. Then, we construct soliton solutions in the CP^2 model with the SU(3) symmetric DM-type interaction. This talk is based on our recent paper arXiv:2101.10566.

### 3rd March 2021, 10am GMT.

#### Jose Queiruga - Some BPS deformations of the Skyrme model

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I will present several deformations of the Skyrme model in three dimensions with self-dual sectors of arbitrary baryonic charge. I will show that, for a family of background metrics as well as for a family of field dependent couplings, the model has one BPS sector, which may have any topological charge. In the gravitating case I will discuss the possible existence of BPS sectors provided that a cosmological constant is added to the model.

### 17th February 2021, 10am GMT.

#### Chris Halcrow - Baby skyrmions from lumps

Watch on YouTube.Consider two baby skyrmions. We understand their interaction when they are widely separated. We also understand what happens when they get close -- they form a ring solution and their individual identities are lost. But how are the separated skyrmions and ring solution connected? How do the degrees of freedom match up as you bring the skyrmions together?

I'll answer this question using lumps, a new approximation which uses a simple map on target space and a new numerical technique. Using these new tools we find new baby skyrmion dynamics and solve the two-baby quantum problem. This is the first time a non-BPS soliton quantum problem has been solved on a manifold with enough degrees of freedom to describe two free solitons.

### 3rd February 2021, 10am GMT.

#### Boris Malomed - Multidimensional solitons

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It is commonly known that the interplay of linear and nonlinear effects gives rise to solitons, i.e., self-trapped localized structures, in a wide range of physical settings, including optics, Bose-Einstein condensates (BECs), hydrodynamics, plasmas, condensed-matter physics, etc. Nowadays, solitons are considered as an interdisciplinary class of modes, which feature diverse internal structures.

While most experimental realizations and theoretical models of solitons have been elaborated in one-dimensional (1D) settings, a challenging issue is prediction of stable solitons in 2D and 3D media. In particular, multidimensional solitons may carry an intrinsic topological structure in the form of vorticity. In addition to the "simple" vortex solitons, fascinating objects featuring complex structures, such as hopfions, i.e., vortex rings with internal twist, have been predicted too.

A fundamental problem is propensity of multidimensional solitons to being unstable (naturally, solitons with a more sophisticated structure, such as vortex solitons, are more vulnerable to instabilities). Recently, novel perspectives for the creation of stable 2D and 3D solitons were brought to the attention of researchers in optics and BEC. The present talk aims to provide an overview of the main results and ongoing developments in this vast field. An essential conclusion is the benefit offered by the exchange of concepts between different areas, such as optics, BEC, and hydrodynamics.

### 16th December 2020, 10am GMT.

#### Andy Royston - Accelerating Solitons

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We review soliton quantization in two-dimensional linear sigma models via the phase space path integral formalism. Working semiclassically, but relaxing the adiabatic assumption, leads to a new saddlepoint equation -- the forced soliton equation -- representing a kink undergoing arbitrary acceleration. We evaluate matrix elements of local operators between soliton states, at leading order in the semiclassical expansion but at arbitrary momentum transfer, in terms of (hypothetical) solutions to the forced soliton equation. Such matrix elements are related, by crossing symmetry, to the creation amplitude for virtual soliton-antisoliton pairs. This talk is based on work done in collaboration with Ilarion Melnikov and Costis Papageorgakis.

### 9th December 2020, 10am GMT.

#### Lorenzo Bartolini - Holographic QCD and Skyrmions

We did not record this seminar. Lorenzo gave a similar seminar at the Henan University Math Phys seminar series, which can be found here.

The holographic duality (also known as Gauge/Strings duality) has proven to be a powerful tool to obtain qualitative and often quantitative insights on the physics of strongly coupled systems. In this talk we review the top-down holographic model of QCD developed by Sakai and Sugimoto (after introducing some basic facts about string theory and QCD) with particular attention to the description of baryons and its ties to the concept of the baryon as a topological soliton. Then we show some recent results we obtained within the model: as a first step we show how a generalized Skyrme model is contained as a low energy limit of the Sakai-Sugimoto model, then we proceed to use the full model with an additional theta-term perturbation to compute the deformation of the baryons and the electric dipole moment it induces for the proton and the neutron (and as a result, for the deuteron). Finally, we provide a short overview of the current research areas on which we are employing the holographic approach and discuss their future directions.

### 2nd December 2020, 10am GMT.

#### Àrpàd Lukàcs - Q-balls in Abelian gauge theories coupled to U(1)×U(1) symmetric scalar fields

Watch on YouTube.

In a series of recent works, Ishihara and Ogawa have investigated nontopological solitons (Q-balls) in a spontaneously broken Abelian gauge theory coupled to two complex scalar fields. The present paper extends their investigations to the most general U(1)×U(1) symmetric quartic potential. Also, a new class of charged Q-ball solutions with vanishing self-interaction terms is investigated and some of their remarkable properties are exhibited.

### 25th November 2020, 10am GMT.

#### Stavros Komineas - Dynamics of skyrmions in ferromagnets

Watch on YouTube.

Both an axially-symmetric topological skyrmion with skyrmion number Q=1 and a non-topological skyrmionium with Q=0 are stable magnetization structures in Dzyaloshinskii-Moriya ferromagnets with easy-axis anisotropy. A topologically trivial (Q=0) configuration in the form of a skyrmion-antiskyrmion pair, called a chiral droplet, is stabilised in the same material.

We study the dynamics of a skyrmion and a skyrmionium under an external field gradient as well as under spin-transfer torque. Our analysis is based on an important link between topology and dynamics which is established through the construction of unambiguous conservation laws. The non-topological Q=0 skyrmionium is accelerated in the direction of the force (the field gradient) thus exhibiting ordinary Newtonian motion. In contrast, the topological Q=1 skyrmion undergoes Hall motion perpendicular to the direction of the force with a drift velocity proportional to it. When the force is switched-off the Q=1 skyrmion is spontaneously pinned whereas the Q=0 skyrmionium continues propagation.

Further, we study the motion of the skyrmionium in the case of spin-transfer torque and observe that this converges to a traveling skyrmionium with a constant velocity. Its velocity is analyzed in two parts: one due to the current flow and a second one acquired by Newtonian acceleration. Similar results are obtained for the chiral droplet.

### 18th November 2020, 10am GMT.

#### Maciej Dunajski - Kinks on a wormhole

Watch on YouTubeThe sine-Gordon equation in 1+1 dimensions admits a static kink solution with with topological charge 1. The kinks do not exist in flat d+1 dimensions, where d>1. I shall prove the existence of static kinks on 3+1 dimensional curved wormhole space-time with two asymptotically flat regions, and discuss linear and non-linear stability of the kinks in the sine-Gordon and \phi^4 theory. This is joint work with Piotr Bizon, Michal Kahl, Michal Kowalczyk and Alice Waterhouse.

### 11th November 2020, 10am GMT.

#### Yasha Shnir - Solitons, Boson stars and Hairy Black Holes

Watch on YouTubeWe study a new families of stationary rotating axially symmetric hairy black holes which represent solutions of the Einstein-Skyrme model in the Kerr spacetime. We found that the spinning axially symmetric cloudy solutions of the model also exist in the regular asymptotically flat space-time without the event horizon. The latter congurations are similar to the usual rotating boson stars, which, in the at flat space limit are linked to the axially symmetric Q-balls, in both cases the solutions exist for some restricted range of values of the angular frequency and possess a quantized angular momentum. Considering similar solution in the O(3) sigma model, we show that, depending on the values of the parameters of the model and the Hawking temperature, the branch structure of the corresponding cloudy solutions varies from the usual inspirraling pattern, which is typical for the boson stars, to the two branch structure, similar to that of the black holes with Skyrme hairs. As another examples of spinning black holes with synchronized hairs we consider families of parity-odd solutions of the Einstein-Klein-Gordon model. Finally, we discuss Dirac stars and compare their properties with the usual boson stars.

### 4th November 2020, 10am GMT.

#### David Ho - The Electroweak Sphaleron in a strong magnetic field

Watch on YouTubeThe Electroweak sphaleron is an unstable solution to the field equations of Electroweak theory and is a source of baryon and lepton number violation in the Standard Model. In this talk, I will present the results of a numerical study into the effect of an external magnetic field on the sphaleron solution. I will show that the sphaleron energy vanishes precisely at the critical field strength where the Higgs symmetry is restored, where there is the potential for unsuppressed baryogenesis. I will also discuss the implications of these results on the possibility of observing sphaleron processes in heavy-ion collisions.

### 28th October 2020, 10am GMT.

Watch on YouTube#### Tomasz Romanczukiewicz - Kinky collisions - are we there yet?

I would like to give an overview of what was done in the past with an emphasis on the most recent discoveries. There are a few new angles that can give us some new insight into these perversely complicated collisions of the simplest topological defects.

### Henan Seminar: 28th October 2020, 2am GMT(UTC).

#### Yong-Liang Ma - Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions in Compact-Star Matter

We discuss the ``sheet structure" of compressed baryonic matter possibly present in massive compact stars in terms of quantum Hall droplets and skyrmions for baryons in medium. The theoretical framework is anchored on a generalized scale symmetric hidden local symmetry that encompasses standard nuclear effective field theory (*s*EFT) and can access the density regimes relevant to massive compact stars. It hints at a basically different, hitherto unexplored structure of the *densest* baryonic matter stable against collapse to black hole. Hidden scale symmetry and hidden local symmetry together in nuclear effective field theory are seen to play a potentially crucial role in providing the hadron-quark duality in compressed baryonic matter.

### 30th September 2020, 10am BST.

#### Rene Garcia-Lara - Asymetric vortex-antivortex pairs of a gauged O(3) Sigma model

Watch on YouTube.Vortices of the gauged O(3) Sigma model are topological solitons appearing after breaking scale invariance in the model with the addition of a convenient potential term. At critical coupling, the model admits BPS static solutions forming a moduli space which carries a complex structure and a Kahler metric. In general, the moduli space of k+ vortices and k- antivortices is incomplete due to the impossibility of a vortex and an antivortex to coalesce. Shifting the vacuum manifold by a constant displacement tau, we obtain an asymmetric model in which vortices and antivortices have different effective mass and size. I will review the model and the L2 metric, and then explain how the governing elliptic problem relates to the properties of the metric for vortices and antivortices on the plane, concluding with some numerical results comparing the properties of the metric for different values of tau.

### 30th September 2020, 10am BST.

#### Marco Barsanti - Near-BPS baby skyrmions and nuclear matter

Watch on YouTube.The Skyrme model is a good candidate for describing the low-energy phase of QCD. It consists of a meson field theory whose static classical solutions are stable due to their geometrical properties. These "collective excitations" of the meson field, known as topological solitons, are called Skyrmions and they are supposed to describe the baryons and nuclei. Beyond the various successful results in the description of the nuclear matter, one of the main problems remains the too large binding energy predicted by the model for the nuclei. To this end, we proposed a field theory, known as "near-BPS model", that is supposed to resolve this problem.

### 23rd September 2020, 10am BST.

#### Miguel Huidobro Garcia and Alberto Garcia Martin-Caro - Neutron star properties from a generalized Skyrme model

Watch on YouTube.In this talk we will review the generalized Skyrme model ---the standard Skyrme model plus the sextic term--- as a suitable description of nuclear matter inside Neutron Stars (NS).

In the first part, we will follow previous approaches to obtain the Equation Of State (EOS) of nuclear matter at supranuclear densities based on Skyrmion crystals as well as fluid-like BPS solutions, and propose a new EOS based on the generalized Skyrme model that takes into account both crystalline and BPS properties at different pressure regimes.

In the second part, we will show how we can constrain the values of the free parameters of this new EOS by fitting some observable properties of stars, such as maximum masses and deformability, to the most recent observations of NS properties from the gravitational wave data of binary NS mergers.

### 16th September 2020, 10am BST.

#### Bruno Barton-Singer - Forces between well-separated magnetic skyrmions

Magnetic skyrmions are topologically non-trivial solutions to the 2D chiral magnet energy functional, similar to baby skyrmions but supported by the first-order Dzyaloshinskii-Moriya interaction (DMI) rather than a fourth-order term. This DMI can be interpreted as an SU(2) gauging of the O(3) sigma model.

Like baby skyrmions, their interaction forces can be calculated asymptotically based on certain approximations, and the DMI leads to an interaction energy that looks like a U(1) gauging of the baby skyrmion interaction energy. In this talk I will derive and apply this formula to a particular case, of skyrmions interacting in a background tilted magnetic field, and compare it to numerical results from the paper 'Turning a chiral skyrmion inside out' . The interaction has an unusual oscillating form.

### 16th September 2020, 10am BST.

#### Calum Ross - Magnetic skyrmions in solvable chiral magnets

In a previous talk in this series we met a two dimensional model of chiral magnets which is of Bogomol'nyi type. I will review this model before discussing a more general model, the solvable line, where we can construct exact single skyrmion solutions. Armed with these exact skyrmion configurations I want to present a first attempt at studying the interactions of these skyrmion configurations. Finally we can use the results about the interaction energy to try to construct a skyrmion lattice state, which is a candidate ground state for the model in particular parameter regions. This is based on joint work with Norisuke Sakai and Muneto Nitta contained in arXiv: 2003.07147.

### 9th September 2020, 10am BST.

#### Nick Manton and Katarzyna Oles - Collective Coordinate Geometry for Kinks and Antikinks

Watch on YouTube.We consider different possibilities for moduli spaces (collective coordinate manifolds) modelling kink-antikink(-kink) dynamics in sine-Gordon and phi^4 theory. The simplest construction based on a superposition of exact kink and antikink solutions can sometimes be improved by including a weight factor and/or by redefining the moduli. This allows us to solve the long-standing null vector problem for the superposed shape modes in phi^4 theory. In certain cases, a kink-antikink collision can be interpreted as a 90-degree scattering of the complexified kink position (separation).

### 2nd September 2020, 10am BST.

#### Jack McKenna - Fermions with background baby Skyrmion on S^2

Watch on YouTube.Fermions coupled to topological solitons can feature zero-energy modes, physically interpreted as bound states where the fermion is localised by the soliton. In some examples of Skyrmions and baby Skyrmions, it is known that these modes have zero energy for a critical value of the coupling constant. On S^3, the fermion coupled to a symmetric Skyrmion features a "chiral shift" where this localised mode, as well as some energy spectra for other modes, are asymmetric in their dependence on the coupling constant. I will briefly discuss my progress and some preliminary results in exploring the analogous system one dimension lower, of a fermion coupled to a baby Skyrmion on S^2.

### 2nd September 2020, 10am BST.

#### Josh Cork - A model for gauged skyrmions with low binding energies

Watch on YouTube.One of the major drawbacks of the Skyrme model is how it severely overestimates nuclear binding energies when compared to experimental results. One of the many proposed modifications for remedying this is a model introduced by Sutcliffe, derived from dimensional reduction of Yang-Mills theory on \mathbb{R}^4. The same approach can be applied to Yang-Mills theory on S^1\times\mathbb{R}^3, from which one obtains an SU(2) gauged Skyrme model. SU(2) instantons on S^1\times\mathbb{R}^3, also known as calorons, are natural examples from which to approximate gauged skyrmions, whose boundary conditions break the gauge group to U(1), and thus provide a natural way to incorporate an electromagnetic field into the Skyrme model. In this talk, I will present some joint work with Derek Harland, and Thomas Winyard, where we consider skyrmions generated from calorons with non-trivial holonomy, which we have used as a 'toy model' for calibrating the gauged model to optimise the ratio Energy/(Lower bound), with a view to developing a U(1) gauged Skyrme model with low binding energies.

### 26th August 2020, 10am BST.

#### Derek Harland and Chris Halcrow - The nucleon-nucleon interaction from Skyrmions

Watch on YouTube.In nuclear physics, one tries to describe the properties of atomic nuclei starting from the nucleon-nucleon (NN) interaction. Hence the NN problem is often called the fundamental problem in nuclear physics and its successful derivation from the Skyrme model would be a major success. Unfortunately, previous attempts have struggled to describe important and well-established features, such as the (isoscalar) spin-orbit interaction. Our new approach overcomes many of these problems. It shows that previous difficulties were a result of over-reliance on the product approximation, rather than problems with the Skyrme model itself.

### 19th August 2020, 10am BST.

#### Andrzej Wereszczynski - The Skyrme model with running coupling constants

Watch on YouTube.I will discuss the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number B = ±1. Higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model.

I will also consider inclusion of the sextic and the potential term and a possible relation with in-medium properties of chiral solitons.

### 12th August 2020, 10am BST.

#### Bernd Schroers - Magnetic Skyrmions andd Chiral Kinks

Chiral magnetic skyrmions are topological solitons in two-dimensional magnetic systems which are stabilised by the Dzyaloshinskii-Moriya interaction (DMI). For each DMI term, there is a model for magnetic skyrmions which is of Bogomol'nyi type and where solitons can be written down explicitly in terms of holomorphic functions. In this talk I will explain how these exact solutions can be used as initial configurations in a numerical scheme to obtain magnetic skyrmions away from the Bogomol'nyi point. This approach reveals a remarkable diversity of magnetic skyrmions and suggests a new way of interpreting their structure. In particular, configurations with positive topological charge are best understood in terms of one-dimensional domain walls carrying chiral kinks. I will explain this point of view, and speculate about possible generalisations. The talk is based on joint work with Vlad Kuchkin, Bruno Barton-Singer, Filipp Rybakov, Stefan Bluegel and Nikolai Kiselev, and on arxiv preprint 2007.06260.