Localization and Attraction

Abstract

We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in $\mathcal{N}=2$, $D=4$ gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in $Ad{S}_4$ which have an $Ad{S}_2\times M_2$ near horizon geometry, where $M_2$ is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in $D=5$ supergravity which have an $Ad{S}_3\times M_2$ near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual $\mathcal{N}=(0,2)$, $d=2$~SCFT.

arXiv comment64 pages. Published version

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Cited by in corpus (5)

• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• Localization of the free energy in supergravity
• NUTs, Bolts, and Spindles
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Kodaira-Spencer Anomalies with Stora-Zumino Method