O(d+1,d+1) enhanced double field theory

TL;DR

This paper develops an enhanced double field theory with O(d+1,d+1) symmetry, enabling consistent reductions of six-dimensional supergravity theories on AdS3×S3, expanding the understanding of T-duality and supergravity truncations.

Contribution

It constructs an O(d+1,d+1) covariant double field theory with novel section constraints and applies it to prove consistent supergravity truncations on AdS3×S3.

Findings

Constructed an enhanced double field theory with internal coordinates in the adjoint of O(d+1,d+1)

Identified two inequivalent solutions to the section constraints for different theories

Proved the consistency of supergravity truncations on AdS3×S3

Abstract

Double field theory yields a formulation of the low-energy effective action of bosonic string theory and half-maximal supergravities that is covariant under the T-duality group O$(d,d)$ emerging on a torus $T^d$. Upon reduction to three spacetime dimensions and dualisation of vector fields into scalars, the symmetry group is enhanced to O$(d+1,d+1)$. We construct an enhanced double field theory with internal coordinates in the adjoint representation of O$(d+1,d+1)$. Its section constraints admit two inequivalent solutions, encoding in particular the embedding of $D=6$ chiral and non-chiral theories, respectively. As an application we define consistent generalized Scherk-Schwarz reductions using a novel notion of generalized parallelization. This allows us to prove the consistency of the truncations of $D=6$, ${\cal N}=(1,1)$ and $D=6$, ${\cal N}=(2,0)$ supergravity on AdS$_3\times \mathbb{S}^3$.