The gauge algebra of double field theory and Courant brackets

TL;DR

This paper explores the gauge algebra of double field theory on a doubled torus, revealing its relation to Courant brackets and T-duality, and clarifies how these symmetries operate despite the Jacobi identity failure.

Contribution

It demonstrates that the gauge algebra in double field theory reduces to the Courant bracket for specific T-dual parameters, connecting it to known mathematical structures.

Findings

The gauge algebra reduces to the Courant bracket for certain parameters.

The gauge transformations are consistent to all orders.

The algebra operates despite the Jacobi identity not holding.

Abstract

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under T-duality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, we find the gauge transformations to all orders and show that the gauge algebra reduces to one obtained by Siegel. We show that the bracket for such restricted parameters is the Courant bracket. We explain how these algebras are realised as symmetries despite the failure of the Jacobi identity.