Microstates of AdS$_5$ black holes with hypermultiplets

TL;DR

This paper constructs and analyzes supersymmetric rotating AdS$_5$ black holes with hypermultiplets, matching their entropy with dual CFT predictions and developing new methods to handle complex extremization equations.

Contribution

It presents the first explicit rotating black hole solutions in 5d $ ext{N}=2$ supergravity with hypermultiplets and verifies their microscopic entropy from dual SCFTs.

Findings

Black hole entropy matches CFT index predictions for specific parameters.

Developed a method to solve complex extremization equations involving hypermultiplets.

Constructed near-horizon geometries perturbatively for nonzero hypermultiplet scalars.

Abstract

We construct supersymmetric rotating AdS$_5$ black holes in 5d $\mathcal{N}=2$ gauged supergravity coupled to two vector multiplets and a universal hypermultiplet, and verify their microscopic counting from the superconformal index of the dual 4d class $\mathcal{S}$ $\mathcal{N}=1$ SCFTs. From the CFT, we perform the Legendre transform of the index to the microcanonical ensemble. The theories are parametrized by a rational number $z$ which enters into the extremization equations making them more challenging to solve. We present a method to address these difficulties and highlight the subtleties involved. From the gravity perspective, we identify a charged, rotating black hole whose Bekenstein-Hawking entropy matches the prediction from the index for $z=\pm1$. Beyond this value, where hypermultiplet scalars are nonzero, we construct the near-horizon extremal geometry perturbatively around $z= 1$ and verify that the entropy is consistent with the CFT prediction. We discuss the thermodynamics and verify the near-horizon versions of the first law of thermodynamics and the supersymmetric condition. In this setting, our analysis characterizes the first construction of a rotating black hole geometry in a 5d $\mathcal{N}=2$ supergravity theory that contains hypermultiplets.