A geometric action for non-geometric fluxes

TL;DR

This paper provides a geometric interpretation of non-geometric Q and R fluxes within double field theory, introducing a higher-dimensional action with kinetic and dual Einstein-Hilbert terms.

Contribution

It offers a novel geometric framework for understanding non-geometric fluxes using a field redefinition related to T-duality in double field theory.

Findings

R flux is a tensor satisfying a Bianchi identity

Q flux acts as a connection covariantizing winding derivatives

Higher-dimensional action includes kinetic term for R flux and dual Einstein-Hilbert term

Abstract

We give a geometrical interpretation of the non-geometric Q and R fluxes. To this end we consider double field theory in a formulation that is related to the conventional one by a field redefinition taking the form of a T-duality inversion. The R flux is a tensor under diffeomorphisms and satisfies a non-trivial Bianchi identity. The Q flux can be viewed as part of a connection that covariantizes the winding derivatives with respect to diffeomorphisms. We give a higher-dimensional action with a kinetic term for the R flux and a 'dual' Einstein-Hilbert term containing the connection Q.