Topological Dirac sigma models and the classical master equation

We present the construction of the classical Batalin-Vilkovisky (BV) 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 to target space covariance, which requires the introduction of two connections with torsion on the Dirac structure.

Automated summary

We present the construction of the classical Batalin-Vilkovisky (BV) action for topological Dirac sigma models, which are two-dimensional topological field theories that simultaneously generalize the completely gauged Wess-Zumino-Novikov-Witten model and the Poisson sigma model. The construction of the BV action for general Dirac sigma models is not applicable using the AKSZ construction, so we follow a direct approach to determine a suitable BV extension of the classical action functional. Special attention is paid to target space covariance, which requires the introduction of two connections with torsion on the Dirac structure.