IIB backgrounds with five-form flux

TL;DR

This paper classifies all N=2 supersymmetric IIB supergravity backgrounds with five-form flux, revealing diverse geometric structures and their relations to known solutions like $AdS_5$ black holes and LLM solutions.

Contribution

It provides a comprehensive classification of supersymmetric IIB backgrounds with five-form flux, detailing their geometric structures and connections to existing solutions.

Findings

Classified backgrounds with $Spin(7)$, $SU(4)$, and $G_2$ stability subgroups.

Identified geometric structures such as almost complex and co-symplectic $G_2$ structures.

Connected known solutions like $AdS_5$ black holes and LLM to specific geometric backgrounds.

Abstract

We investigate all N=2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups $Spin(7)\ltimes\bR^8$, $SU(4)\ltimes\bR^8$ and $G_2$. In the $SU(4)\ltimes\bR^8$ case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the $SU(4)\ltimes \bR^8$ structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The $G_2$ backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic $G_2$ structure. The $Spin(7)\ltimes\bR^8$ backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy $Spin(7)$. In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the $AdS_5$ black holes, lift to $SU(4)\ltimes\bR^8$ pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one $G_2$ manifold which has principal orbit $S^3\times S^3$.