Generalised Structures for $\mathcal{N}=1$ AdS Backgrounds

TL;DR

This paper demonstrates that generic minimally supersymmetric AdS backgrounds in warped flux compactifications can be characterized by a simple weak integrability condition within the framework of $E_{d(d)}\times\mathbb{R}^+$ generalised geometry, linking supersymmetry to geometric structures.

Contribution

It introduces a unified geometric description of supersymmetric AdS backgrounds using generalised $G$-structures with constant intrinsic torsion, extending previous understanding.

Findings

AdS backgrounds correspond to spaces with generalised $G$-structures.

Supersymmetry conditions are equivalent to a weak integrability condition.

The approach simplifies the classification of supersymmetric flux backgrounds.

Abstract

We expand upon a claim made in a recent paper [arXiv:1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak integrability condition in the language of $E_{d(d)}\times\mathbb{R}^+$ generalised geometry. Namely, they are spaces admitting a generalised $G$-structure set by the Killing spinor and with constant singlet generalised intrinsic torsion.