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SIG X (Solitons @ Work workshop)

20 June - 01 July 2022

From classical to quantum Solitons

Lectures on topological solitons, their mathematical properties and physical applications.

As always, the aim of this informal workshop is to increase interactions (and possible future collaboration) between topological solitons oriented physicists and mathematicians. So, we are mainly focused on discussion.

This year we want once again to discuss problems and open questions related to dynamical aspects of topological solitons, their interactions and quantization.

Due to the Russian attack on Ukraine and still unstable COVID situation, the workshop will be held in a hybrid form with all talks avaliable online. However, we do our best to keep the informal spirit of the workshop where the stress is put on the discussion rather than talks. The participation is free and open to everyone. To join the workshop and the workshop mailing list please e-mail Kasia Oles at katarzyna.slawinska [at]

The first week will have even more informal climate with only one talk a day, also avaliable online. In addition, the talks will have more introduction/overview flavour. Therefore they should be especially interesting for students.

In the second week, which is the main week of the workshop, we plan to have (only) 2 online talks every day followed by informal (almost unlimited) discussion sessions.

This edition is again organized within the framework Soliton at Work S@W.

We acknowledge financial support from:
  • the Faculty of Physics, Astronomy and Applied Computer Science of the Jagiellonian University.
  • the Department of Field Theory, Institute of Theoretical Physics of the Jagiellonian University
  • NAWA Polish National Agency for Academic Exchange

    Invited speakers and topics

    The second week

  • Zoltan Bajnok (Budapest) / Marton Lajer (Brookhaven), "Bootstrapping and measuring S-matrices and form factors"
  • Piotr Bizon (Krakow), "Soliton resolution conjecture"
  • Jorge Castelo (Santiago), "Universal relations for rotating boson stars"
  • Patrick Dorey (Durham) and Tom Romanczukiewicz (Krakow), "Collisions of weakly-bound kinks "
  • Jarah Evslin (Lanzhou), "A Less Powerful Approach to Quantum Kinks"
  • Luiz Ferreira (Sao Carlos), "A Quasi Self-Dual Skyrme Model"
  • Peter Forgacs (Budapest/Tours), Arpad Lucacs (Durham),"Q-balls: Something old and something new, with components one and two"
  • Alberto Garcia Martin-Caro (Santiago), "Kaon condensation and strangeness in compact skyrme stars"
  • Bjarke Gudnason (Henan), "Nineteen vortex equations and integrability"
  • Chris Halcrow (Stockholm/Leeds), "Instanton-generated skyrmions for nuclear physics"
  • Nick Manton (Cambridge), "Skyrmion Challenges from Nuclear Physics"

    The first week

  • Bruno Barton-Singer (Edinburgh), "Magnetic skyrmion stability"
  • Dominik Ciurla (Krakow), "Bose-Einstein condensate and a negative radiation pressure"
  • Miguel Huidobro (Santiago), "Skyrme crystals"
  • Paul Leask (Leeds), "Skyrmion crystals"
  • Carlos Naya (Stockholm) "Hunting 3D solitons in frustrated magnets"
  • Jose Queiruga (Salamanca), "Domain wall strings"
  • Andy Royston (Penn U.), "Quantum Solitons: A Review of the Canonical Transformation Approach"
  • Yasha Shnir (Oldenburg), "Boson stars and hairy black holes"
  • Martin Speight (Leeds), "Geometry of vortices on the sphere in the dissolving limit"
  • Andrzej Wereszczynski (Krakow), "Kink collisions: an overview"

    After each talk there will be an informal (unlimited) discussion session. There will be speacial rooms devoted for the discussion, which can be freely enterd and left.

    Program 27 June - 01 July

    Monday Tuesday Wednesday Thursday Friday
    10.50 welcome
    11.00 Nick Jarah Peter and Arpad Patrick and Tom Bjarke
    15.00 Zoltan and Marton Piotr Jorge/Alberto Chris Luiz
    16.30 closing remarks

    The hours are given for the European time zone. For UK -1 (10 am/14 pm). For China + 6 (5 pm/9 pm). For Brazil -5 (6 am/10 am)

    Program 20 June - 24 June

    Monday Tuesday Wednesday Thursday Friday
    11.00 Andrzej Andy Miguel / Paul Martin Bruno
    16.00 Dominik Yasha Jose Carlos

    Open Problems

    We encourage the speakers to propose open problems which may give some inspiration for all participants


  • Skyrmion shapes and nuclear shapes.

    Both nuclei and Skyrmions are known to spontaneously break rotational symmetry -- i.e. have a shape. This is restored by quantisation, giving definite spins, but the details are different. Nuclear shapes are mainly just ellipsoids or occasionally pear-shapes, though alpha-particle clusters are more subtle. Nuclear vibrations are widespread throughout the nuclear chart too. Skyrmions have (complicated and interesting) shapes arising more naturally. The challenge for Skyrmion theory is to quantatively understand the energy spectra more fundamentally. This includes shapes, vibrational frequencies, moments of inertia. These parameters are largely phenomenological in nuclear theory, e.g. vibrational modes are related to 1p-1h, particle-hole excitations (or better, 2p-2h) but the actual energies (frequencies) are much less than double the nearby shell model gaps. There are many even-even 'spherical' nuclei around B=100 (Ru-104 is a nice example) with clear quadrupole multi-phonons of frequency about 0.5 MeV, and also an octupole 3^- state at about 2 MeV which might be an octupole phonon or a tetrahedral rigid-body state. Can this be understood using Skyrmions? For smaller nuclei like Carbon-12 our work is quite successful, but we are largely playing catch-up with older work going back to Wheeler/Wefelmeier, Bohr/Mottelson and the more recent Bijker/Iachello papers. How can we jump ahead?

  • Intrinsic pion field structure.

    Skyrmions spontaneously break isospin symmetry, captured by their 'colouring'. The idea that nuclei spontaneously break isospin symmetry and that collective quantisation restores it is completely revolutionary, and most nuclear physicists don't believe it. Can we find convincing evidence? Some places to look are (i) the correlations between spin and isospin allowed states, (ii) a theory of the strength of spin-orbit coupling, (iii) a collective picture for beta decay as dominated by an isospin raising/lowering transition within an isospin multiplet. We have a few good results on these topics: spin/isospin spectra for B=4,6,7,8,12 not bad, and isospin inertias scale the right way as B increases further (the B=10 spectrum needs a further bending mode). An experimentalist assured me that not seeing the predicted (embarrassing) 0^- state in Lithium-8 (1 second lifetime) is not too surprising -- could be produced through M2 transition from known 2^+ state, but what is rate and could it be observed in radioactive beam? Alternatively, maybe this state disappears through more careful quantisation of two B=8 Skyrmions. Spin-orbit coupling partly understood for N-N and for single Skyrmion coupled to planar layer, but need to deal with single Skyrmion coupled to a (round) cluster with high symmetry -- what orbital angular momenta occur? Can round layer be modelled by rational map?


  • Does the perturbative relativistic CCM description converge to the full field theory? Under which circumstances?
  • Is the repulsive interaction between kink and antikink with fat tails (e.g., in \phi^8 theory) related to spectral walls? I think so!
  • What is the role of radiation in the fractal structure observed in kink-antikink collisions. Include radiation in a CCM!

    Nick and Q-balls

  • It would be good to clarify which soliton theories admit exact time-dependent, periodic solutions. A conjecture is that such a solution must be strictly sinusoidal with one frequency, and that's only possible by exploiting an internal U(1) symmetry. So Q-balls, isospinning hopfions, spinning baby Skyrmions, dyons, spinning Skyrmions can exist, provided the frequency is below the meson mass threshold. Shape-mode-oscillating kinks, and oscillons are not exact solutions because the oscillation is anharmonic and couples nonlinearly to the radiation. Remaining questions (and apologies if some answers are well-known): Why can't one have a strictly sinusoidal shape-mode oscillation (this is clear in a collective coordinate picture, but not obvious more generally)? Is the sG breather strictly sinusoidal in a suitable variable? Does the target space have to be compact (as Martin proposed)? What happens if the U(1) action is gauged and there's a massless photon (a Higgs mechanism may be essential to make the photon massive)? Can the the classical action over one period be used for an approximate quantisation, and does this relate to electric charge quantisation in a gauged theory? Does semiclassical quantisation of the action lead automatically to quantisation of spin and/or isospin in the cases where the relevant rotation/isorotation groups are SO(3), or something else nonabelian and compact, and not gauged?


  • 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 the inclusion of this contribution corrects the energy and also produces the appearance of the pasta phase structures in the Skyrme model.

    Participants (76)

  • Christoph Adam (Santiago de Compostela)
  • Alexis Roa Aguirre (Itajuba)
  • Markus Amano (Henan)
  • Yuki Amari (Tokyo)
  • Bruno Barton-Singer (Edinburgh)
  • Zoltan Bajnok (Budapest)
  • Marco Barsanti (Pisa)
  • Lorenzo Bartolini (Pisa)
  • Anxo Biasi (Krakow)
  • Piotr Bizon (Krakow)
  • Filip Blaschke (Praha/Opava)
  • Stefano Bolognesi (Pisa)
  • Rodolfo Casana (Maranho)
  • Jorge Castelo (Santiago de Compostela)
  • Gautam Chaudhuri (Leeds)
  • Michal Ciesla (Krakow)
  • Dominik Ciurla (Krakow)
  • Josh Cork (Hannover)
  • Bradley Cownden (Krakow)
  • Tomasz Dobrowolski (Krakow)
  • Patrick Dorey (Durham)
  • Jarah Evslin (Lanzhou/Bejin)
  • Manfred Faber (Vienna)
  • Luiz Ferreira (Sao Carlos)
  • Peter Forgacs (Budapest/Tours)
  • Vakhid Gani
  • Rene Garcia (Mexico)
  • Alberto Garcia Martin-Caro (Santiago de Compostela)
  • Shubham Garg (Jodhpur, India))
  • Jacek Gatlik (Krakow)
  • Adalto R. Gomes (Maranhao)
  • Bjarke Gudnason (Hennan)
  • Fernando Miguel Hahne (Florianopolis)
  • Chris Halcrow (Leeds/Stockholm)
  • Derek Harland (Leeds)
  • Eduardo da Hora (Maranhao)
  • Miguel Huidobro (Santiago de Compostela)
  • Alberto Izquierdo (Salamanca)
  • Romuald Janik (Krakow)
  • Yu Jiahui (Henan)
  • Ondrej Karpisek (Opava)
  • Pawel Klimas (Florianopolis)
  • Marco Kneipp (Florianopolis)
  • Steffen Krusch (Canterbury, Kent U.)
  • Fred C. Lima (Maranhao)
  • Paul Leask (Leeds)
  • Leandro Roza Livramento
  • Marton Lajer (Brookhaven, BNL)
  • Arpad Lucacs (Durham)
  • Jack Mckenna (Canterbury, Kent U.)
  • Nick Manton (Cambridge)
  • Francisco Marinho (Vila Real)
  • Alejandro Mata Ali (Santiago de Compostela)
  • Azadeh Mohammadi (Pernambuco)
  • Carlos Naya (Stockholm)
  • Maciej Nowak (Krakow)
  • Kasia Oles (Krakow)
  • Jose Queiruga (Salamanca)
  • Tomek Romanczukiewicz (Krakow)
  • Calum Ross (London)
  • Andy Royston (Penn U., US)
  • Giacomo Santori (Rome)
  • Caroline dos Santos
  • Daniel Santos (Rio de Janerio)
  • Yasha Shnir (Oldenburg)
  • Fabiano Simas (Maranhao)
  • Martin Speight (Leeds)
  • Lukasz Stepien (Krakow)
  • Paul Sutcliffe (Durham)
  • Ricardo Vazquez (Santiago de Compostela)
  • Mateusz Wachla (Krakow)
  • Andrzej Wereszczynski (Krakow)
  • Tom Winiard (Canterbury)
  • Wojtek Zakrzewski (Durham)
  • Baiyang Zhang (Minneapolis)
  • Zhang Tiantian (Henan)

    Advisory board

  • Christoph Adam (Santiago de Compostela)
  • Bjarke Gudnason (Henan)
  • Chris Halcrow (Leeds/Stockholm)

    Local organizing committee

  • K. Oles (Krakow)
  • T. Romanczukiewicz (Krakow)
  • A. Wereszczynski (Krakow)

    Online room details

    This woskshop will be held on-line using the Zoom platform. We encourage the participants to use the newest Zoom version. Here are details of the meeting platform are:
  • Meeting ID:
  • Passcode:


    katarzyna.slawinska [at], andrzej.wereszczynski [at]