Microstates of rotating AdS${}_5$ strings

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 $T^2\times S_{\omega }^2$, 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.

arXiv comment31 pages; v2: typos corrected

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• Anomalies, Black strings and the charged Cardy formula
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• N=(0,4) Black String Chains
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• The Surprising Effectiveness of Weyl Gravity in Probing Quantum Corrections to AdS Black Holes
• 4d F(4) gauged supergravity and black holes of class $\mathcal{F}$
• Universal AdS black holes in theories with sixteen supercharges and their microstates
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• The Near-Horizon Geometry of Supersymmetric Rotating AdS${}_4$ Black Holes in M-theory
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• New supersymmetric $Ad{S}_5$ black strings from 5D $N=4$ gauged supergravity
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Supersymmetric AdS${}_6$ black holes from ISO(3)xU(1) F(4) gauged supergravity