A ten-dimensional action for non-geometric fluxes

TL;DR

This work demonstrates that the NSNS sector of ten-dimensional supergravity can be reformulated, via a Generalized Complex Geometry–inspired field redefinition to a tilde basis $(\tilde g,\tilde\beta,\tilde\phi)$, to reveal a ten-dimensional $Q$-flux without introducing new degrees of freedom. Under a simplifying assumption that $\tilde{\beta}$ aligns with isometry directions, the NSNS Lagrangian in the tilde variables matches a $Q$-flux–only form up to a total derivative, allowing a standard dimensional reduction that reproduces the familiar $|Q|^2$ contribution to the 4D scalar potential. The paper further analyzes global issues, derives ten-dimensional equations of motion and Bianchi identities in the tilde basis, and connects to four-dimensional EFTs and double field theory, arguing for a preferred, globally well-defined basis in non-geometric settings. These results bridge the gap between ten- and four-dimensional descriptions of non-geometry and provide a concrete pathway to incorporate non-geometric fluxes into a higher-dimensional, low-energy effective framework. The approach offers a promising route to systematically study non-geometric backgrounds and their phenomenological implications, while outlining future work on including R-flux and RR sectors, and exploring a DFT formulation. Finally, the work reinforces the view that non-geometry can be understood within a well-defined ten-dimensional framework without introducing extra degrees of freedom, by appropriate field redefinitions guided by Generalized Complex Geometry.

Abstract

The NSNS Lagrangian of ten-dimensional supergravity is rewritten via a change of field variables inspired by Generalized Complex Geometry. We obtain a new metric and dilaton, together with an antisymmetric bivector field which leads to a ten-dimensional version of the non-geometric Q-flux. Given the involved global aspects of non-geometric situations, we prescribe to use this new Lagrangian, whose associated action is well-defined in some examples investigated here. This allows us to perform a standard dimensional reduction and to recover the usual contribution of the Q-flux to the four-dimensional scalar potential. An extension of this work to include the R-flux is discussed. The paper also contains a brief review on non-geometry.