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Low

Energy

Effective

Dynamics of

Skyrmions

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A conference on skyrmions, topological solitons, and nuclear physics.

2nd-5th July 2018, University of Leeds

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Monday 2nd Tuesday 3rd Wednesday 4th Thursday 5th
Chemistry LT D Maths MALL Maths MALL Maths MALL
09.30 Krusch 09.30 Zakrzewski 09.30 Lau 09.30 Naya
10.15 Flood 10.15 Ioannidou 10.15 Freer 10.15 Gudnason
11.00 COFFEE 11.00 COFFEE 11.00 COFFEE 11.00 COFFEE
11.30 Sutcliffe 11.30 Schroers 11.30 Dobaczewski 11.30 Stevenson
12.30 LUNCH 12.30 LUNCH 12.30 LUNCH 12.30 LUNCH
13.30 Marrows 13.30 Ross
14.15 Foster 14.15 Franchetti 14.00 Wereszczynski 14.00 Petri
15.00 TEA 15.00 TEA 15.00 TEA 15.00 TEA
15.30 Winyard 15.30 Cork 15.30 Manton 15.30 Halcrow
16.15 Shnir 16.15 Ferreira 16.15 Speight 16.15 Harland
18.00 conference dinner

Room locations and directions

Monday: Chemistry Lecture Theatre D Look for the Parkinson building on Woodhouse Lane: it's a large white neoclassical building with a wide staircase at its main entrance. From the main entrance, walk up hill and enter at the next (much smaller) entrance. Lecture Theatre D is almost immediately in front of you.

Tuesday-Thursday: School of Maths MALL: enter campus on Willow Terrace Road. Follow this until just past the swimming pool, turn right to pass a pond, then turn left and head up the ramp. You'll find yourself in a square, with the School of Maths diagonally opposite. The MALL is on level 8.

See also the campus map.

The conference dinner will be on Wednesday 4th at 6pm at Sous le Nez on Quebec Street.

Jacek Dobaczewski Nuclear Density Functional Theory and its selected applications
Numerous applications of nuclear DFT have shown a tremendous success of the approach, which by using a dozen-odd coupling constants allows for correct description of a multitude of nuclear phenomena. However, recent analyses indicate that the currently used models have probably reached their limits of precision and extrapolability. The question of whether these can be systematically improved appears to be one of the central issues of the present-day investigations in nuclear-structure theory. In this talk, I will present status of theoretical developments that aim to build novel nonlocal energy density functionals (EDFs), illustrated by a selection of results.

Josh Cork Skyrmions and calorons
Some time ago, Atiyah and Manton proposed a method of approximating Skyrme fields as the holonomy of a Yang-Mills instanton along all lines in one direction of R^4. This proves to be a very good approximation, and more recently, Sutcliffe has provided an explanation for its strength by utilising techniques inspired by holographic constructions. Calorons are instantons for which one direction is periodic, and one may produce a candidate for a Skyrme field analogously as the holonomy along this periodic direction. Viewing this caloron approximation in light of Sutcliffe's work, one sees that the natural object to compare calorons to are really gauged skyrmions. In this talk, we shall describe a one-parameter family of gauged Skyrme models which tend to the ordinary Skyrme model in a particular limit (the one corresponding to an infinitely periodic caloron), and shall present some numerical results regarding spherically symmetric fields with a comparison to the caloron approximations.

Luiz Ferreira Exact Self-Dual Skyrmions from Rational Map and Conformal Ansaetze
We consider a recently proposed modified Skyrme model possessing an exact self-dual sector. In such a model the SU(2) generators in the quadratic and quartic terms in the action are contracted with a 3x3-matrix of fields, instead of the usual trace form. We show that any rational map configuration of any topological charge is an exact self-dual Skyrmion solution. In addition, we use the conformal symmetry of the theory to build a toroidal ansatz that also leads to exact self-dual Skyrmions of any charge. The toroidal Skyrmions differ in shape from the rational map solutions in the sense that they do not present radial holes in their topological charge densities.

Stephen Flood Chern-Simons Vortices on Compact Domains
Vortices arising in the Abelian Higgs model have been well studied due to their relation applications in condensed matter physics and cosmology and as analogues to aid in understanding more complicated solitons in higher dimensions. Vortices in models with a Chern-Simons term are of further interest, since they carry both an electric and magnetic charge, allowing them to describe phenomena such as the fractional quantum hall effect. I will discuss vortices in two such Chern-Simons models allowing a BPS structure, focusing on compact domains and presenting some numerical results on the 2-sphere.

David Foster Composite Skyrmion bags in two-dimensional materials
Skyrmions have been experimentally observed in magnetic and liquid crystal systems, where they form as individual objects. I will outline how we extended a technique from HEP Skyrmions to magnetic Skyrmions, which describes how Skyrmions interact. I will then discuss how this led to the realisation of a new composite Skyrmion, which we verify by simulation in magnetic systems and by experiment in liquid crystals. This talk will be based on the results in arXiv:1806.02576.

Guido Franchetti Hyperbolic multi Taub-NUT and monopoles
In this talk, based on G. Franchetti and R. Maldonado J. Math. Phys. 57 (2016), p. 073502 arXiv:1603.09575, I will show how to obtain hyperbolic monopoles from the dimensional reduction of circle-invariant instantons. The procedure is very well known in the case of circle invariant instantons on the 4-sphere, but I will consider instead instantons on a different space, which I like to call hyperbolic multi Taub-NUT. Suitable projections of the Levi-Civita connection of conformally rescaled multi Taub-NUT yield two classes of monopoles. The first one depends on a function satisfying a hyperbolic version of the Helmholtz equation. It can be shown to reproduce those monopoles which arise from the JNR ansatz, but the construction still offers interesting insights. The second class is a 1-parameter family of genuinely new solutions.

Martin Freer Title
This contribution describes the latest developments in the field of light nuclei and explores how the tendency of nucleons to cluster into alpha-particle subunits influences their structure. In particular there is a focus on the structure of the nucleus 12C and in turn its link to nucleosynthesis and the formation of organic life.

Derek Harland Roll skyrmions and the spin-orbit force
I will discuss my recent paper with Nick Manton on our progress in extracting the spin-orbit force from the Skyrme model.

Sven Bjarke Gudnason Classical and quantum binding energies in generalized Skyrme models

Chris Halcrow The B=5 Skyrmion as a two-cluster system
In the shell model, the B=5 nucleus is described by a two-cluster system: an alpha particle core is orbited by a single nucleon. Similarly, in many Skyrme models, the B=5 Skyrmion can be approximated by a core B=4 plus an additional B=1. Taking this approximation seriously, one can attempt to quantise the 4+1 system in an approach inspired by moduli space quantisation. In this talk, I will do so in the limit where the clusters interact weakly. The actual results are disappointing but the method provides lessons on the spin-orbit force and the importance of discrete symmetries in the Skyrme model, and suggest a regime where the Skyrme and shell models may match.

Theodora Ioannidou Wormholes immersed in rotating matter
We consider four-dimensional wormholes immersed in bosonic matter. Their existence is based on the presence of a phantom field, however, many of their interesting physical properties are be-stowed upon them by an ordinary complex scalar field, which carries only a mass term, but no self-interactions. For instance, the rotation of the scalar field induces a rotation of the throat as well. Moreover, the bosonic matter need not be symmetrically distributed in both asymptotically flat regions, leading to symmetric and asymmetric rotating wormhole spacetimes. The presence of the rotating matter also allows for wormholes with a double throat.

Steffen Krusch Introducing Topological Solitons
In this talk I give an overview of the area of topological solitons. I introduce the topological degree and how it is used to classify solitons. I briefly mention the moduli space approximation with vortices as an example. Then I describe approaches to quantising the Skyrme model and how to calculate ground and excited states of atomic nuclei.

Chris Lau Baryon constraint in the Sakai-Sugimoto model
Sakai-Sugimoto model is a top-down holographic qcd model. Baryons are described by instanton solutions in the model. The model has many successes such as the reproduction of chiral anomaly, computation of properties of baryons etc.. However, Hata and Murata pointed out and showed that one important baryon constraint which is responsible for selecting the correct 3-flavour baryon multiplets cannot be derived from the model. In the talk, I will present our proposed solution and show how it can help recover the required constraint while preserving the other features in the hqcd model.

Chris Marrows Electrical Hall signals from individual skyrmions in Pt/Co/Ir multilayer discs

Nicholas Manton Skyrmions old and new
The landscape of multi-Skyrmion solutions becomes more complicated as the baryon number increases. I will review progress on finding selected, symmetric examples, many with baryon numbers for which solutions were previously unknown. The lightly bound Skyrme model has provided useful insight here, and has also been helpful in a recent investigation by Derek Harland and myself of spin-orbit coupling in the Skyrme model.

Carlos Naya-Rodriguez The BPS Skyrme Model of Vector Mesons and the Pion Mass Revolution
The Skyrme model is a low energy effective field theory of QCD where pions are the fundamental degrees of freedom whereas baryons appear as their collective excitations. In this talk, we will focus on the coupling of the Skyrme field to other hadrons (concretely vector mesons), especially on the model proposed by Prof. Paul Sutcliffe where a BPS bound (a lower topological bound on the energy) is fulfilled if an infinite tower of vector mesons is included. Due to the complexity of the energy functional, this is a highly demanding numerical problem and even for one vector meson exact solutions for light nuclei besides the baryon number one had not been found so far. Here, the first exact results when the first vector meson is included are presented. They are in consonance with previous calculations by using the instanton approximation and where with just the first vector meson added the energy considerably decreased close to the BPS bound. To conclude, preliminary results when the pion mass term is included will be also presented.

Marina Petri Lifetime measurements in neutron-rich C and O isotopes to advance the ab initio frontier
Ab initio nuclear structure theories using 2- (NN) and 3-body (3N) Hamiltonians derived from chiral Effective Field Theory (EFT) connect to the underlying physics of the strong interaction and provide a unique opportunity to understand the nuclear structure and its evolution from first principles. Although recent calculations of excitation energies with chiral NN+3N interactions in light and medium-mass (mainly closed-shell) nuclei have been successful, their extension to other observables remains a challenge. Therefore, new data on electromagnetic properties provide an exciting opportunity to constrain NN+3N Hamiltonians derived from chiral EFT in ab initio calculations ranging from Nuclear Lattice EFT to the No-Core Shell Model.
Two experiments have been performed with the goal to extract lifetimes of excited states in 16 C and 21 O. These lifetimes are particularly sensitive to the details of the nuclear interaction used, and can discriminate between phenomenological and realistic interactions. Excited states in 16 C were populated using a fusion-evaporation reaction at the ATLAS facility, Argonne National Laboratory and lifetimes were extracted using the Doppler Shift Attenuation Method; for this experiment Gammasphere was coupled to the Microball array. Excited states in 21 O were populated via a multi-nucleon removal reaction at the National Superconducting Cyclotron Laboratory using the S800 spectrometer and GRETINA. Results from both experiments will be presented.

Jonathan Rawlinson Skyrmions, Quantum Graphs and Carbon-12

Calum Ross Hyperbolic vortices and flat connections
Certain integrable vortex equations admit an interpretation as the flatness condition for a non-abelian connection. Focusing on hyperbolic vortices the flat connection is valued in the Lie algebra of SU(1,1), the pseudo unitary group. This can be lifted to a flat connection on the three dimensional group manifold which can in turn be related to maps from SU(1,1) to itself. From these flat connections massless solutions of Dirac equations on SU(1,1) and 2+1 dimensional Minkowski space can be constructed.

Bernd Schroers Vortices and synthetic gauge fields from Skyrme configurations
Maps from Euclidean 3-space to SU(2) of quadratic degree and satisfying a certain holomorphicity condition can be used to construct both vortices on the 2-sphere and zero-modes of the Dirac operator in Euclidean 3-space. I will review this construction (first given in a joint paper with Calum Ross), and then explain how an analogous but approximate construction can be used to realise linked and knotted synthetic gauge fields in two-level atoms interacting with a laser beam.

Yasha Shnir Soliton solutions of the gauged baby Skyrme model

Martin Speight Mass splitting in the Skyrme model
It is not straightforward to account for the difference in mass between the proton and the neutron within the Skyrme model. Previous explanations introduce multiple couplings to several extra mesons (the omega, rho and eta mesons), or invoke sophisticated ideas from holography and an explicit up-down quark mass difference. I will argue that the mass difference can be generated by adding a single extra term to the standard omega meson variant of the Skyrme model, involving no extra fields (beyond the pion and omega meson). The Skyrmion that emerges has, to leading order, unperturbed pion and omega^0 fields, but acquires a small azimuthal omega^i field localized around its equator.

Paul Stevenson Nuclear collisions and resonances from time-dependent density-functional theory
Density-functional theory (DFT) using Skyrme-type interactions is able to well-reproduce ground state properties of nuclei. By using the time-dependent version of DFT, one can study processes such as fusion, fission, and the collective excitation of single nuclei. In this talk we explore the results of such calculations, looking at how one extracts useful information about the effective interaction, about the inherent limitations of DFT, and about the physical processes themselves.

Paul Sutcliffe Magnetic Skyrmions and Hopfions
A magnetic Skyrmion is a nanoscale topological soliton that can be realized experimentally in certain magnetic materials. I shall discuss some properties of magnetic Skyrmions and present numerical evidence for the existence of related magnetic Hopfions.

Andrzej Wereszczynski Neutron stars from the Skyrme model perspective

Thomas Winyard The effects of anisotropy in multicomponent vortex models
While Anisotropy has the effect of a spatial rescaling in single component models, in multi-component models this is no longer the case. I will show that anisotropy leads to new physics, such as novel field configurations from additional couplings, direction dependent interactions and novel bound states that could be seen in experiment. Additionally I will suggest that the physics we predict can be used to explain long standing questions from experimental multi-component systems.

Wojtek Zakrzewski BPS equations for interacting scalar field theories in (1+1) dimensions
We study BPS systems, in (1+1) dimensions, involving more than one field. We discuss the conditions that have to be imposed on various terms in Lagrangians involving many fields to produce BPS systems and then look in detail at the simplest of such cases.
We analyse in detail a BPS system involving 2 sine-Gordon like fields and study its properties when we take its solitonic static solutions and use them as initial conditions for their evolution in Lorentz covariant versions of the model. We also discuss other, more general, such systems and relate the properties of their solitonic solutions to the vacua of such models.