Redefining B-twisted topological sigma models

TL;DR

This paper presents a new approach to the B-twist in topological sigma models on Kähler manifolds, providing a clearer BRST interpretation and emphasizing the role of auxiliary fields for off-shell closure.

Contribution

It introduces an alternative B-twist procedure that enhances the understanding of topological sigma models and clarifies the role of auxiliary fields in their algebraic structure.

Findings

Provides a proper BRST interpretation of the B-twisted sigma model.

Highlights the importance of auxiliary fields for off-shell closure.

Offers an alternative description of Witten's topological sigma model.

Abstract

A recently proposed variation on the usual procedure to perform the topological B-twist in rigid $N=2$ models is applied to the case of the $\sigma $ model on a K\"ahler manifold. This leads to an alternative description of Witten's topological $\sigma $ model, which allows for a proper BRST interpretation and ghost number assignement. We also show that the auxiliary fields, which are responsible for the off shell closure of the $N=2$ algebra, play an important role in our construction.