\beta-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework

TL;DR

The paper introduces eta-supergravity, a ten-dimensional theory incorporating non-geometric fluxes, providing a geometric framework and linking it to four-dimensional gauged supergravities through generalized geometry.

Contribution

It develops the eta-supergravity theory with a geometric interpretation of non-geometric fluxes and explores its relations to lower-dimensional supergravities and solutions.

Findings

Identification of Q- and R-fluxes in the NSNS sector

Reproduction of the ten-dimensional Lagrangian using Generalized Geometry

Discussion of solutions and symmetries of the theory

Abstract

We present a ten-dimensional theory, named \beta-supergravity, that contains non-geometric fluxes and could uplift some four-dimensional gauged supergravities. Building on earlier work, we study here its NSNS sector, where Q- and R-fluxes are precisely identified. Interestingly, the Q-flux is captured in an analogue of the Levi-Civita spin connection, giving rise to a second curvature scalar. We reproduce the ten-dimensional Lagrangian using the Generalized Geometry formalism; this provides us with enlightening interpretations of the new structures. Then, we derive the equations of motion of our theory, and finally discuss further aspects: the dimensional reduction to four dimensions and comparison to gauged supergravities, the obtention of ten-dimensional purely NSNS solutions, the extensions to other sectors and new objects, the supergravity limit, and eventually the symmetries, in particular the \beta gauge transformation. We also introduce the related notion of a generalized cotangent bundle.