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Journal of High Energy Physics

, 2016:74 | Cite as

A supersymmetric Skyrme model

  • Sven Bjarke Gudnason
  • Muneto Nitta
  • Shin Sasaki
Open Access
Regular Article - Theoretical Physics

Abstract

Construction of a supersymmetric extension of the Skyrme term was a long-standing problem because of the auxiliary field problem; that is, the auxiliary field may propagate and cannot be eliminated, and the problem of having fourth-order time derivative terms. In this paper, we construct for the first time a supersymmetric extension of the Skyrme term in four spacetime dimensions, in the manifestly supersymmetric superfield formalism that does not suffer from the auxiliary field problem. Chiral symmetry breaking in supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions) but also in the same number of quasi-NG bosons so that the low-energy theory is described by an SL(N, \( \mathrm{\mathbb{C}} \))-valued matrix field instead of SU(N) for NG bosons. The solution of auxiliary fields is trivial on the canonical branch of the auxiliary field equation, in which case our model results in a fourth-order derivative term that is not the Skyrme term. For the case of SL(2, \( \mathrm{\mathbb{C}} \)), we find explicitly a nontrivial solution to the algebraic auxiliary field equations that we call a non-canonical branch, which when substituted back into the Lagrangian gives a Skyrme-like model. If we restrict to a submanifold, where quasi-NG bosons are turned off, which is tantamount to restricting the Skyrme field to SU(2), then the fourth-order derivative term reduces exactly to the standard Skyrme term. Our model is the first example of a nontrivial auxiliary field solution in a multi-component model.

Keywords

Supersymmetric Effective Theories Solitons Monopoles and Instantons 

Notes

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.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Sven Bjarke Gudnason
    • 1
  • Muneto Nitta
    • 2
  • Shin Sasaki
    • 3
  1. 1.Institute of Modern PhysicsChinese Academy of SciencesLanzhouChina
  2. 2.Department of Physics, and Research and Education Center for Natural SciencesKeio UniversityYokohamaJapan
  3. 3.Department of PhysicsKitasato UniversitySagamiharaJapan

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