G-structures for black hole near-horizon geometries

TL;DR

This paper characterizes conditions for supersymmetric warped AdS2 solutions in Type II supergravity, introduces new classes of solutions with specific internal geometries, and analyzes their fluxes and structures.

Contribution

It provides a comprehensive analysis of supersymmetric AdS2 solutions, deriving new classes in Type IIA and Type IIB supergravity with detailed geometric and flux conditions.

Findings

Derived conditions for supersymmetric warped AdS2 solutions.

Constructed new classes of solutions with G2 and SU(3) structures.

Expressed fluxes and fields in terms of torsion classes.

Abstract

We derive necessary and sufficient conditions for warped AdS$_2$ solutions of Type II supergravity to preserve ${\cal N}=1$ supersymmetry, in terms of bispinors. Such solutions generically support an SU$(3)$-structure on their internal manifold M$_8$, which can experience an enhancement to a G$_2$-structure. We perform an SU$(3)$-structure torsion classes analysis and express the fluxes and other physical fields in terms of these, in general. We use our results to derive two new classes of AdS$_2$ solutions. In (massive) Type IIA supergravity we derive an ${\mathcal N}=1$ supersymmetric class for which M$_8$ decomposes as a weak G$_2$-manifold foliated over an interval and which is locally defined in terms of a degree three polynomial. In Type IIB supergravity we find a class of AdS$_2\times\text{S}^2\times\text{CY}_2\times\Sigma_2$ solutions preserving small ${\cal N}=4$ supersymmetry, governed by a harmonic function on $\Sigma_2$ and partial differential equations reminiscent of D3-D7-brane configurations.