Topological Sigma Models with H-Flux

TL;DR

This paper explores a topological sigma model twisted from an N=(2,2) supersymmetric theory with a bihermitian target space, introducing a generalized topological term linked to gerbes, and ensuring global quantum consistency.

Contribution

It introduces a new topological sigma model with H-flux, generalizing the A-model by incorporating gerbe connections and Wilson surfaces for global well-definedness.

Findings

The action is Q-exact plus a quasi-topological term.

The quasi-topological term is related to a flat gerbe-connection.

Exponentiating the term yields a Wilson surface, ensuring global consistency.

Abstract

We investigate the topological theory obtained by twisting the N=(2,2) supersymmetric nonlinear sigma model with target a bihermitian space with torsion. For the special case in which the two complex structures commute, we show that the action is a Q-exact term plus a quasi-topological term. The quasi-topological term is locally given by a closed two-form which corresponds to a flat gerbe-connection and generalises the usual topological term of the A-model. Exponentiating it gives a Wilson surface, which can be regarded as a generalization of a Wilson line. This makes the quantum theory globally well-defined.