Abstract
We consider the Skyrme model in the near-BPS limit. The BPS part is made of the sextic term plus a potential and the deformation is made of the standard massive Skyrme model controlled by a small parameter ϵ ≪ 1. In order to keep the perturbation under theoretical and computational control, we find a model for which BPS Skyrmions have compact support, henceforth denoted as compactons, and the spherically symmetric B = 1 Skyrmion represents the most stable solution. We use the ϵ-expansion scheme to systematically calculate the corrections to the energy and compare with the exact numerical computations in the B = 1 sector. Finally, we use the ϵ-expansion scheme to calculate the bound state of two B = 1 Skyrmions and its binding energy, which corresponds, prior to quantization, to the deuteron in our model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T.H.R. Skyrme, A Nonlinear field theory, Proc. Roy. Soc. Lond. A 260 (1961) 127 [INSPIRE].
T.H.R. Skyrme, A Unified Field Theory of Mesons and Baryons, Nucl. Phys. 31 (1962) 556 [INSPIRE].
E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].
E. Witten, Current Algebra, Baryons, and Quark Confinement, Nucl. Phys. B 223 (1983) 433 [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
G.S. Adkins, C.R. Nappi and E. Witten, Static Properties of Nucleons in the Skyrme Model, Nucl. Phys. B 228 (1983) 552 [INSPIRE].
C.J. Halcrow, Vibrational quantisation of the B = 7 Skyrmion, Nucl. Phys. B 904 (2016) 106 [arXiv:1511.00682] [INSPIRE].
S. Bjarke Gudnason and C. Halcrow, Vibrational modes of Skyrmions, Phys. Rev. D 98 (2018) 125010 [arXiv:1811.00562] [INSPIRE].
S.B. Gudnason and C. Halcrow, A SMörgåsbord of Skyrmions, JHEP 08 (2022) 117 [arXiv:2202.01792] [INSPIRE].
B. Zumino, Supersymmetry and Kähler Manifolds, Phys. Lett. B 87 (1979) 203 [INSPIRE].
E.A. Bergshoeff, R.I. Nepomechie and H.J. Schnitzer, Supersymmetric Skyrmions in Four-dimensions, Nucl. Phys. B 249 (1985) 93 [INSPIRE].
A.A. Bogolubskaya and I.L. Bogolubsky, Stationary Topological Solitons in the Two-dimensional Anisotropic Heisenberg Model With a Skyrme Term, Phys. Lett. A 136 (1989) 485 [INSPIRE].
A.A. Bogolyubskaya and I.L. Bogolyubsky, On stationary topological solitons in two-dimensional anisotropic Heisenberg model, Lett. Math. Phys. 19 (1990) 171 [INSPIRE].
B.M.A.G. Piette, B.J. Schroers and W.J. Zakrzewski, Multi - solitons in a two-dimensional Skyrme model, Z. Phys. C 65 (1995) 165 [hep-th/9406160] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
S. Bolognesi and W. Zakrzewski, Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Extended Supersymmetry and BPS solutions in baby Skyrme models, JHEP 05 (2013) 108 [arXiv:1304.0774] [INSPIRE].
M. Nitta and S. Sasaki, BPS States in Supersymmetric Chiral Models with Higher Derivative Terms, Phys. Rev. D 90 (2014) 105001 [arXiv:1406.7647] [INSPIRE].
M. Nitta and S. Sasaki, Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models, Phys. Rev. D 91 (2015) 125025 [arXiv:1504.08123] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, A supersymmetric Skyrme model, JHEP 02 (2016) 074 [arXiv:1512.07557] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, Topological solitons in the supersymmetric Skyrme model, JHEP 01 (2017) 014 [arXiv:1608.03526] [INSPIRE].
S.B. Gudnason, M. Barsanti and S. Bolognesi, Near-BPS baby Skyrmions, JHEP 11 (2020) 062 [arXiv:2006.01726] [INSPIRE].
P. Sutcliffe, Skyrmions, instantons and holography, JHEP 08 (2010) 019 [arXiv:1003.0023] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A Skyrme-type proposal for baryonic matter, Phys. Lett. B 691 (2010) 105 [arXiv:1001.4544] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A BPS Skyrme model and baryons at large Nc, Phys. Rev. D 82 (2010) 085015 [arXiv:1007.1567] [INSPIRE].
D. Harland, Topological energy bounds for the Skyrme and Faddeev models with massive pions, Phys. Lett. B 728 (2014) 518 [arXiv:1311.2403] [INSPIRE].
C. Adam, K. Oles and A. Wereszczynski, The Dielectric Skyrme model, Phys. Lett. B 807 (2020) 135560 [arXiv:2005.00018] [INSPIRE].
P. Sutcliffe, Skyrmions in a truncated BPS theory, JHEP 04 (2011) 045 [arXiv:1101.2402] [INSPIRE].
C. Naya and P. Sutcliffe, Skyrmions in models with pions and rho mesons, JHEP 05 (2018) 174 [arXiv:1803.06098] [INSPIRE].
M. Gillard, D. Harland and M. Speight, Skyrmions with low binding energies, Nucl. Phys. B 895 (2015) 272 [arXiv:1501.05455] [INSPIRE].
N.S. Manton and P. Sutcliffe, Topological solitons, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2004), https://doi.org/10.1017/CBO9780511617034 [INSPIRE].
S.B. Gudnason, Dielectric Skyrmions, Phys. Rev. D 102 (2020) 116013 [arXiv:2009.03082] [INSPIRE].
S.B. Gudnason, M. Barsanti and S. Bolognesi, Near-BPS baby Skyrmions with Gaussian tails, JHEP 05 (2021) 134 [arXiv:2102.12134] [INSPIRE].
E. Bonenfant and L. Marleau, Nuclei as near BPS-Skyrmions, Phys. Rev. D 82 (2010) 054023 [arXiv:1007.1396] [INSPIRE].
E. Bonenfant, L. Harbour and L. Marleau, Near-BPS Skyrmions: Non-shell configurations and Coulomb effects, Phys. Rev. D 85 (2012) 114045 [arXiv:1205.1414] [INSPIRE].
J.M. Speight, Near BPS Skyrmions and Restricted Harmonic Maps, J. Geom. Phys. 92 (2015) 30 [arXiv:1406.0739] [INSPIRE].
R. Battye and P. Sutcliffe, Skyrmions and the pion mass, Nucl. Phys. B 705 (2005) 384 [hep-ph/0410157] [INSPIRE].
R. Battye and P. Sutcliffe, Skyrmions with massive pions, Phys. Rev. C 73 (2006) 055205 [hep-th/0602220] [INSPIRE].
S.B. Gudnason and M. Nitta, Fractional Skyrmions and their molecules, Phys. Rev. D 91 (2015) 085040 [arXiv:1502.06596] [INSPIRE].
S.B. Gudnason and M. Nitta, A higher-order Skyrme model, JHEP 09 (2017) 028 [arXiv:1705.03438] [INSPIRE].
B.J. Schroers, Dynamics of moving and spinning Skyrmions, Z. Phys. C 61 (1994) 479 [hep-ph/9308236] [INSPIRE].
S.B. Gudnason and J.M. Speight, Realistic classical binding energies in the ω-Skyrme model, JHEP 07 (2020) 184 [arXiv:2004.12862] [INSPIRE].
G.L. Greene, E.G. Kessler, R.D. Deslattes and H. Boerner, New Determination of the Deuteron Binding Energy and the Neutron Mass, Phys. Rev. Lett. 56 (1986) 819 [INSPIRE].
V.B. Kopeliovich and B.E. Stern, Exotic Skyrmions, JETP Lett. 45 (1987) 203 [INSPIRE].
N.S. Manton, Is the B = 2 Skyrmion Axially Symmetric?, Phys. Lett. B 192 (1987) 177 [INSPIRE].
J.J.M. Verbaarschot, Axial Symmetry of Bound Baryon Number Two Solution of the Skyrme Model, Phys. Lett. B 195 (1987) 235 [INSPIRE].
S.B. Gudnason and M. Nitta, Modifying the pion mass in the loosely bound Skyrme model, Phys. Rev. D 94 (2016) 065018 [arXiv:1606.02981] [INSPIRE].
S.B. Gudnason, B. Zhang and N. Ma, Generalized Skyrme model with the loosely bound potential, Phys. Rev. D 94 (2016) 125004 [arXiv:1609.01591] [INSPIRE].
S.B. Gudnason, Exploring the generalized loosely bound Skyrme model, Phys. Rev. D 98 (2018) 096018 [arXiv:1805.10898] [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
C. Adam and A. Wereszczynski, Topological energy bounds in generalized Skyrme models, Phys. Rev. D 89 (2014) 065010 [arXiv:1311.2939] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2206.09559
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Gudnason, S.B., Barsanti, M. & Bolognesi, S. Near-BPS Skyrmions. J. High Energ. Phys. 2022, 92 (2022). https://doi.org/10.1007/JHEP11(2022)092
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)092