Microscopic Entropy of AdS${}_3$ Black Holes Revisited

Abstract

We revisit the microscopic description of AdS${}_3$ black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS${}_3$/CFT${}_2$ correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is not respected by individual states. This interpretation provides a microscopic understanding of the hitherto mysterious charge constraints satisfied by all BPS black holes in AdS. We also develop thermodynamics and a nAttractor mechanism of AdS${}_3$ black holes in the nearBPS regime.

arXiv comment35 pages, 1 figure

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• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• The Phase Diagram of BPS Black Holes in AdS${}_5$
• Localization on $Ad{S}_3\times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity