Daniel Waldram, Imperial College
Supersymmetric backgrounds and generalised geometry
Supersymmetric backgrounds of type II and eleven dimensional supergravity including flux degrees of freedom provide natural generalisations of the notion of a manifold with special holonomy. The classic example is that of a generalised Calabi—Yau manifold introduced by Hitchin and Gualtieri, which defines an integrable structure on the sum of the tangent and cotangent spaces. We will discuss how a version of generalised geometry with an E_d structure group gives a unified description of the supergravity fields such that supersymmetric backgrounds correspond to torsion-free generalised structures. This defines the generic string theoretic extension of Calabi—Yau and Sasaki—Einstein geometries, among others. As an application, we discuss the moduli spaces of the “exceptional Sasaki—Einstein” geometries that are the generic duals of N=1 superconformal field theories.