Spindle black holes in AdS$_4 \times$SE$_7$

TL;DR

This paper constructs new supersymmetric AdS$_2 imes ext{spindle}$ solutions in 4d gauged supergravity, linking black hole entropy to geometric data and providing holographic insights into certain 3d SCFT indices.

Contribution

It introduces a novel class of supersymmetric solutions with charged hypermultiplets on spindle geometries, and derives a general formula for gravitational blocks in 4d ${ m extbf{N}=2}$ supergravity.

Findings

Black hole entropy from gravitational block gluing.

Explicit solutions with charged scalars on spindle geometries.

Holographic computation of the spindle index for ${ m extbf{N}=2}$ theories.

Abstract

We construct new classes of supersymmetric AdS$_2 \times {\Sigma}$ solutions of 4d gauged supergravity in presence of charged hypermultiplet scalars, with ${\Sigma}$ the complex weighted projective space known as a spindle. These solutions can be viewed as near-horizon geometries of asymptotically Anti de-Sitter (AdS$_4$) black holes with magnetic fluxes that admit embedding in 11d on Sasaki-Einstein (SE$_7$) manifolds, which renders them of holographic interest. We show that in each case the Bekenstein-Hawking entropy follows from the procedure of gluing two gravitational blocks, ultimately determined by SE$_7$ data. This allows us to establish the general form of the gravitational blocks in gauged 4d ${\mathcal N} =2$ supergravity with charged scalars and massive vectors. Holographically, our results provide a large N answer for the spindle index with anti-twist and additional mesonic or baryonic fluxes of a number of ${\mathcal N} =2$ Chern-Simons-matter theories.