Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 2, Pages 1-21Publisher
SPRINGER
DOI: 10.1007/JHEP02(2016)074
Keywords
Supersymmetric Effective Theories; Solitons Monopoles and Instantons
Categories
Funding
- Recruitment Program of High-end Foreign Experts
- KAKENHI from the the Ministry of Education, Culture, Sports, Science (MEXT) of Japan [15H05855, 15H00841]
- Japan Society for the Promotion of Science (JSPS) (KAKENHI) [25400268]
- MEXT [S1511006]
- Kitasato University
- Grants-in-Aid for Scientific Research [15H00841, 15H05855] Funding Source: KAKEN
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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, )-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, ), 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.
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