Gauging the nonlinear sigma-model through a non-Abelian algebra

TL;DR

This paper extends the BFFT method to transform the nonlinear sigma model into a non-Abelian gauge theory, demonstrating the compatibility with supersymmetry and addressing algebra locality issues.

Contribution

It introduces a non-Abelian extension of the BFFT method for the nonlinear sigma model, including supersymmetric cases, and discusses algebra locality.

Findings

Supersymmetric sigma model is compatible only with non-Abelian gauge theory.

The standard BFFT method results in a nonlocal algebra for the supersymmetric case.

The bosonic case was previously considered with Abelian gauging.

Abstract

We use an extension of the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) for transforming the nonlinear $\sigma$ model in a non-Abelian gauge theory. We deal with both supersymmetric and nonsupersymmetric cases. The bosonic case was already considered in literature but just gauged with an Abelian algebra. We show that the supersymmetric version is only compatible with a non-Abelian gauge theory. The usual BFFT method for this case leads to a nonlocal algebra.