Dirac sigma models from gauging the nonlinear sigma models and its BV action

TL;DR

This paper constructs Dirac sigma models by gauging 2D nonlinear sigma models, explores metric couplings, and develops their classical BV action, providing a comprehensive framework for these models.

Contribution

It introduces a systematic construction of Dirac sigma models including their BV action, emphasizing the uniqueness of minimal metric coupling.

Findings

Minimal coupling to the metric sector is generally the only nontrivial option.

The classical BV action for Dirac sigma models is explicitly constructed.

The approach ensures the BV action satisfies the classical master equation.

Abstract

We present the construction of the Dirac sigma models by gauging the 2-dimensional nonlinear sigma models, but also including the possibility of nonminimal coupling to the metric sector. We show that for a large variety of possible cases, the minimal coupling to the metric sector is the only nontrivial possibility. In addition, we present the construction of the classical Batalin-Vilkovisky action for the Dirac sigma models. We follow a direct approach in its construction, by requiring it to be a solution of the classical master equation.