U-dual fluxes and Generalized Geometry

TL;DR

This paper systematically analyzes string flux compactifications using Exceptional Generalized Geometry, revealing new deformations of supergravity backgrounds and providing explicit superpotential expressions for various flux configurations.

Contribution

It establishes a precise map between fluxes, gaugings, and EGG, identifying all gaugings that uplift to 10d backgrounds and introducing new deformations like RR counterparts of the $eta$-deformation.

Findings

Identified the complete set of gaugings with 10d uplift potential.

Discovered new deformations extending the $eta$-deformation to F-theory.

Derived explicit superpotential expressions for flux compactifications.

Abstract

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the $\beta$-deformation. These new deformations are expected to provide the natural extension of the $\beta$-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.