Spindle black holes and theories of class $\mathcal{F}$

TL;DR

This paper constructs new $AdS_2\times\Sigma$ solutions with spindle geometries in 4d supergravity, computes their entropy, and validates the gravitational block approach for dual 3d superconformal field theories in class $\mathcal{F}$.

Contribution

It introduces explicit spindle solutions in 4d supergravity and demonstrates their consistency with dual field theory predictions using gravitational blocks.

Findings

Successfully constructed $AdS_2\times\Sigma$ solutions with spindle geometries.

Computed Bekenstein-Hawking entropy matching dual field theory predictions.

Validated gravitational block approach for scalar fields and entropy calculations.

Abstract

We construct solutions in the form of $AdS_2\times\Sigma$, where $\Sigma$ denotes a spindle geometry, within a particular 4d $\mathcal{N}=2$ gauged supergravity with vector multiplets and a charged hypermultiplet stemming from a consistent truncation of 6d matter coupled $F(4)$ gauged supergravity on a Riemann surface. We also compute the Bekenstein-Hawking entropy for the presumed asymptotically $AdS_4$ black hole solutions, providing a dual prediction for the spindle index of 3d superconformal field theories falling under the class $\mathcal{F}$. Notably, the gravitational block description of the solutions accurately replicates the entropy and the values of scalar fields at the two orbifold points of the spindle, validating our findings.