Gauged Courant sigma models

TL;DR

This paper introduces gauged Courant sigma models (GCSMs), extending Courant sigma models with additional gauge symmetries linked to Lie groups, groupoids, and algebroids, ensuring consistency through geometric identities.

Contribution

It develops a new class of sigma models incorporating gauge symmetries related to Lie and Courant algebroids, expanding the framework of AKSZ-type models.

Findings

GCSMs incorporate gauge symmetries from Lie groups, groupoids, and algebroids.

Consistency conditions are expressed as flatness identities on the target space.

Analysis of GCSMs with fluxes and boundaries reveals new geometric structures.

Abstract

We propose a new class of sigma models based on Courant sigma models. We refer to these models as gauged Courant sigma models (GCSMs). By introducing additional gauge symmetries, such as those associated with a Lie group, a Lie groupoid (or Lie algebroid), and a Courant algebroid on the target space, Courant sigma models are extended to gauged sigma models of AKSZ type. The consistency of the theory is ensured by identities among geometric quantities on Lie algebroids and Courant algebroids, such as curvatures and torsions, which can be interpreted as flatness conditions on the target space. We also analyze geometric structures of GCSMs in the presence of fluxes and boundaries.