Flux Backgrounds and Exceptional Generalised Geometry

TL;DR

This thesis explores flux compactifications in string theory using exceptional generalised geometry, focusing on dimensional reductions, deformations for Romans mass, and supersymmetry-preserving truncations.

Contribution

It develops a framework for flux compactifications with exceptional generalised geometry, including adaptations for type IIA supergravity and the Romans mass.

Findings

Constructed exceptional generalised geometry for type IIA supergravity.

Identified deformations of the generalised Lie derivative for Romans mass.

Applied generalised Scherk-Schwarz method for consistent truncations.

Abstract

The main topic of this thesis are flux compactifications. Firstly, we study dimensional reductions of type II and eleven-dimensional supergravities using exceptional generalised geometry. We start by presenting the needed mathematical tools, focusing on G-structures and their extension to generalised geometry. Then, we move our focus on compactifications. In particular, we mainly focus on type IIA, building the version of exceptional generalised geometry adapted to such supergravity and finding the right deformations of generalised Lie derivative to accomodate the Romans mass. We describe the generalised Scherk-Schwarz method to find consistent truncation ansatze preserving the maximal amount of supersymmetry. As further point, we study generalised calibrations on AdS backgrounds in type IIB and M-theory.