Generalised Geometry and Flux Vacua

TL;DR

This paper explores how generalised geometry offers a unified mathematical framework to describe flux compactifications in string theory, including supersymmetry constraints, RR fields, and non-geometric backgrounds, leading to explicit flux compactification examples.

Contribution

It demonstrates how generalised geometry reformulates supersymmetry conditions and extends to RR fields and non-geometric backgrounds, providing new tools for flux compactification analysis.

Findings

Supersymmetry constraints expressed as integrability conditions in generalised complex geometry

Exceptional generalised geometry geometrizes RR fields

Construction of explicit flux compactification examples

Abstract

This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.