Large Gauge Transformations in Double Field Theory

TL;DR

This paper explores the structure of large gauge transformations in double field theory, revealing their composition properties and connection to the Courant bracket, which impacts how symmetries are understood in this framework.

Contribution

It introduces a new interpretation of finite gauge transformations as generalized coordinate transformations and analyzes their algebraic properties, including non-associativity.

Findings

Transformations form a group on fields but not on coordinates

Large transformations can be expressed via derivatives of coordinate maps

Composition of transformations involves the Courant bracket

Abstract

Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.