Dirac Sigma Models

TL;DR

The paper introduces the Dirac Sigma Model, a new topological field theory that generalizes existing models like the Poisson sigma model and G/G-WZW model, with a focus on Lie algebroid morphisms and topological invariants.

Contribution

It presents a novel topological sigma model based on Courant algebroids, unifying and extending previous models such as the Poisson sigma model and G/G-WZW model.

Findings

The model's equations of motion correspond to Lie algebroid morphisms.

The kinetic term acts as a regulator but is optional in the Poisson case.

The gauge invariant content remains independent of additional structures at the classical level.

Abstract

We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.