# Gauging as constraining: the universal generalised geometry action in two dimensions

## TL;DR

This paper reviews a generalized approach to constructing gauge actions in two-dimensional sigma models using foliation and Dirac structures, without requiring global symmetries, and employs advanced geometric frameworks.

## Contribution

It introduces a novel method for gauging sigma models via foliation and Dirac structures, extending the traditional symmetry-based approach without needing global symmetries.

## Key findings

- Reformulation of ungauged theories with auxiliary fields in the generalized tangent bundle.
- All gauge theories arise from restricting auxiliary fields to Dirac structures.
- Establishment of a geometric framework using Lie algebroids, Courant algebroids, and Dirac structures.

## Abstract

One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to include gauge fields. In this contribution we review the construction of gauged actions for two-dimensional sigma models, considering a more general notion to be gauged, namely that of a (possibly singular) foliation. In particular, the original action does not need to have any global symmetry for this purpose. Moreover, reformulating the ungauged theory by means of auxiliary 1-form fields taking values in the generalised tangent bundle over the target, all possible such gauge theories result from restriction of these fields to take values in (possibly small) Dirac structures. This turns all the remaining 1-form fields into gauge fields and leads to the presence of a local symmetry. We recall all needed mathematical notions, those of (higher) Lie algebroids, Courant algebroids, and Dirac structures.