A supersymmetric Skyrme model

TL;DR

This paper constructs the first supersymmetric extension of the Skyrme model in four dimensions using superfield formalism, overcoming the auxiliary field problem and deriving a Skyrme-like term with explicit solutions.

Contribution

It introduces a novel supersymmetric Skyrme model with a nontrivial auxiliary field solution, extending the Skyrme term within superfield formalism without auxiliary field issues.

Findings

Explicit nontrivial auxiliary field solution found for SL(2,C)

The model reduces to the standard Skyrme term under certain restrictions

First example of a nontrivial auxiliary field solution in a multi-component model

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,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,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.