Topological Dirac Sigma Models and the Classical Master Equation

TL;DR

This paper constructs the classical BV action for topological Dirac sigma models, a class of 2D topological field theories generalizing several models, focusing on their geometric structure and covariance properties.

Contribution

It provides the first explicit BV extension for Dirac sigma models, addressing the challenge of target space covariance with torsion connections.

Findings

Successfully constructed the BV action satisfying the classical master equation.

Highlighted the geometric structure involving Dirac manifolds and Courant algebroids.

Addressed the limitations of AKSZ construction for these models.

Abstract

We present the construction of the classical Batalin-Vilkovisky action for topological Dirac sigma models. The latter are two-dimensional topological field theories that simultaneously generalise the completely gauged Wess-Zumino-Novikov-Witten model and the Poisson sigma model. Their underlying structure is that of Dirac manifolds associated to maximal isotropic and integrable subbundles of an exact Courant algebroid twisted by a 3-form. In contrast to the Poisson sigma model, the AKSZ construction is not applicable for the general Dirac sigma model. We therefore follow a direct approach for determining a suitable BV extension of the classical action functional with ghosts and antifields satisfying the classical master equation. Special attention is paid on target space covariance, which requires the introduction of two connections with torsion on the Dirac structure.