Beyond the standard gauging: gauge symmetries of Dirac Sigma Models

TL;DR

This paper explores the gauge symmetries of Dirac Sigma Models, allowing for more general background fields and relaxing isometry conditions, thereby broadening the understanding of gauge invariance in two-dimensional field theories.

Contribution

It introduces a framework for gauge symmetries in Dirac Sigma Models using Lie algebroids and Courant algebroids, extending the class of gauge-invariant theories beyond traditional isometry constraints.

Findings

Gauge invariance can be achieved without Killing vector fields.

Connections on Lie algebroids determine gauge symmetries.

Dirac structures in Courant algebroids underpin the gauge symmetry formulation.

Abstract

In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic sigma-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac sigma-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.