Generalised Cosets

TL;DR

This paper extends the framework of generalised geometry to double coset spaces, enabling new consistent truncations of supergravity and applications to specific string theory backgrounds.

Contribution

It introduces a method to construct generalised frames and connections on double coset target spaces, broadening the scope of generalised geometry in string theory.

Findings

Construction of generalised frame fields on double cosets

Development of a generalised covariant derivative with constant intrinsic torsion

Application to supergravity truncations and string theory backgrounds

Abstract

Recent work has shown that two-dimensional non-linear $\sigma$-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to target spaces constructed as double cosets $M=\widetilde{G} \backslash D / H$. Mirroring conventional coset geometries, we show that on $M$ one can construct a generalised frame field and a $H$-valued generalised spin connection that together furnish an algebra under the generalised Lie derivative. This results naturally in a generalised covariant derivative with a (covariantly) constant generalised intrinsic torsion, lending itself to the construction of consistent truncations of 10-dimensional supergravity compactified on $M$. An important feature is that $M$ can admit distinguished points, around which the generalised tangent bundle should be augmented by localised vector multiplets. We illustrate these ideas with explicit examples of two-dimensional parafermionic theories and NS5-branes on a circle.