Twisted R-Poisson Sigma Models

TL;DR

This paper introduces twisted R-Poisson sigma models, a class of topological field theories that generalize Poisson models and address the limitations of the AKSZ formalism in the presence of Wess-Zumino terms.

Contribution

It extends the AKSZ formalism to twisted R-Poisson sigma models, showing how to solve the classical master equation without a QP structure.

Findings

Generalization of Poisson sigma models to twisted R-Poisson models

Connection to differential graded manifolds and higher geometry

Method to identify solutions to the classical master equation

Abstract

The AKSZ construction was developed as a geometrical formalism to find the solution to the classical master equation in the BV quantization of topological branes based on the concept of QP manifolds. However, the formalism does not apply in presence of Wess-Zumino terms, as demonstrated recently by Ikeda and Strobl in the simplest example of WZW-Poisson sigma models. In this contribution, we review a class of topological field theories in arbitrary dimensions, the twisted R-Poisson sigma models, which suitably generalize Poisson or twisted Poisson sigma models. Their relation to differential graded manifolds and higher geometry is discussed and we sketch how to identify the solution to the classical master equation even though the target space does not have a QP structure.