Generalized geometric vacua with eight supercharges

TL;DR

This paper explores flux compactifications of type II and M-theory to $AdS_5$ with eight supercharges using Exceptional Generalized Geometry, deriving integrability conditions that generalize Sasaki-Einstein structures.

Contribution

It formulates supersymmetry conditions as integrability conditions for generalized structures in Exceptional Generalized Geometry, extending known geometric frameworks.

Findings

Derived generalized integrability conditions for supersymmetric $AdS_5$ compactifications.

Connected Killing-spinor equations to geometric integrability conditions.

Extended geometric descriptions to include fluxes and gauge fields.

Abstract

We investigate compactifications of type II and M-theory down to $AdS_5$ with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped $AdS_5$ background imply the generalized integrability conditions.