Abstract
We study the supersymmetric extensions of the O(3) σ-model in 1+1 and 2+1 dimensions. We show that it is possible to construct non-equivalent supersymmetric versions of a given model sharing the same bosonic sector and free from higher-derivative terms.
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References
A.M. Polyakov, Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields, Phys. Lett. B 59 (1975) 79 [INSPIRE].
A.M. Polyakov and A.A. Belavin, Metastable States of Two-Dimensional Isotropic Ferromagnets, JETP Lett. 22 (1975) 245 [INSPIRE].
L. Álvarez-Gaumé and D.Z. Freedman, Geometrical Structure and Ultraviolet Finiteness in the Supersymmetric σ-model, Commun. Math. Phys. 80 (1981) 443 [INSPIRE].
L. Álvarez-Gaumé and D.Z. Freedman, Potentials for the Supersymmetric Nonlinear σ-model, Commun. Math. Phys. 91 (1983) 87 [INSPIRE].
B. Zumino, Supersymmetry and Kähler Manifolds, Phys. Lett. B 87 (1979) 203 [INSPIRE].
E. Witten, A Supersymmetric Form of the Nonlinear σ-model in Two-Dimensions, Phys. Rev. D 16 (1977) 2991 [INSPIRE].
E. Witten and D.I. Olive, Supersymmetry Algebras That Include Topological Charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].
P. Di Vecchia and S. Ferrara, Classical Solutions in Two-Dimensional Supersymmetric Field Theories, Nucl. Phys. B 130 (1977) 93 [INSPIRE].
E. Witten, Constraints on Supersymmetry Breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982) 661 [INSPIRE].
J. Bagger, Supersymmetric sigma models, in Supergravities in diverse dimensions, vol. 1, A. Salam and E. Sezgin eds., pg. 569-611 (1989).
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].
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].
S. Bolognesi and W. Zakrzewski, Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [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].
J.M. Queiruga, Baby Skyrme model and fermionic zero modes, Phys. Rev. D 94 (2016) 065022 [arXiv:1606.02869] [INSPIRE].
J.M. Queiruga, Skyrme-like models and supersymmetry in 3 + 1 dimensions, Phys. Rev. D 92 (2015) 105012 [arXiv:1508.06692] [INSPIRE].
J.M. Queiruga, Supersymmetric galileons and auxiliary fields in 2 + 1 dimensions, Phys. Rev. D 95 (2017) 125001 [arXiv:1612.04727] [INSPIRE].
E.R.C. Abraham and P.K. Townsend, Intersecting extended objects in supersymmetric field theories, Nucl. Phys. B 351 (1991) 313 [INSPIRE].
P. Rossi, Fermion Zero Modes and Hidden Symmetry, Phys. Lett. B 71 (1977) 145 [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, T. Romanczukiewicz, J. Sanchez-Guillen and A. Wereszczynski, Investigation of restricted baby Skyrme models, Phys. Rev. D 81 (2010) 085007 [arXiv:1002.0851] [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].
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].
M. Andrews, M. Lewandowski, M. Trodden and D. Wesley, Distinguishing k-defects from their canonical twins, Phys. Rev. D 82 (2010) 105006 [arXiv:1007.3438] [INSPIRE].
D. Bazeia, J.D. Dantas, A.R. Gomes, L. Losano and R. Menezes, Twinlike Models in Scalar Field Theories, Phys. Rev. D 84 (2011) 045010 [arXiv:1105.5111] [INSPIRE].
C. Adam and J.M. Queiruga, An algebraic construction of twin-like models, Phys. Rev. D 84 (2011) 105028 [arXiv:1109.4159] [INSPIRE].
C. Adam and J.M. Queiruga, Twinlike models with identical linear fluctuation spectra, Phys. Rev. D 85 (2012) 025019 [arXiv:1112.0328] [INSPIRE].
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Queiruga, J.M., Wereszczynski, A. Non-uniqueness of the supersymmetric extension of the O(3) σ-model. J. High Energ. Phys. 2017, 141 (2017). https://doi.org/10.1007/JHEP11(2017)141
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DOI: https://doi.org/10.1007/JHEP11(2017)141