Welcome to the Geometric Models of Nuclear Matter Digital Seminar Series. Originally, we planned to hold a conference at the University of Kent in 2020. Due to the global health situation, this has been postponed. Hopefully we can meet in summer 2021.

The seminar series is now over. However, it has grown into a project to keep the soliton community connected during the rest of the pandemic. This is Solitons at Work (or Soltions@Work if you work in marketing). You can see what's going on with that at www.solitonsatwork.net.

## Past Seminars

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

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

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.

*and*

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

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.

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

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

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.

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

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.

*and*

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

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.

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

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

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.

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

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.

*and*

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

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.

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

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

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 - Jagiellonian University - The Skyrme model with coupling functions - watch - slides

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 - Heriot-Watt University - Magnetic Skyrmions andd Chiral Kinks - slides

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.## More information

The conference is supported by the London Mathematical Society.

The series is organised by Steffen Krusch and Chris Halcrow.