Microstates of rotating AdS$_5$ strings

TL;DR

This paper derives a formula for the refined topologically twisted index of certain gauge theories on D3-branes, and uses it to microscopically explain the entropy of rotating black strings in AdS$_5$ via supergravity solutions.

Contribution

It introduces a general formula for the refined topologically twisted index in the Cardy limit and connects it to rotating black string entropy through explicit supergravity solutions.

Findings

Derived a general formula for the twisted index in the Cardy limit.

Constructed rotating domain-wall solutions in five-dimensional supergravity.

Provided a microscopic explanation for black string entropy using the index.

Abstract

We provide a general formula for the refined topologically twisted index of $\mathcal{N}=1$ gauge theories living on the world-volume of D3-branes at conical Calabi-Yau singularities in the Cardy limit. The index is defined as the partition function on $T^2 \times S^2_\omega$, with a partial topological twist and a $\Omega$-deformation along $S^2$, in the presence of background magnetic fluxes and fugacities for the global symmetries and can be used to study the properties of a class of BPS black strings. To this purpose, we find rotating domain-wall solutions of five-dimensional gauged supergravity interpolating between AdS$_5$ and a near horizon region consisting of a warped fibration of BTZ over a sphere. We explicitly construct rotating domain-walls that can be embedded in AdS$_5 \times S^5$ by uplifting a class of four-dimensional rotating black holes. We then provide a microscopic explanation of the entropy of such black holes by using the refined topologically twisted index of $\mathcal{N}=4$ super Yang-Mills.