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Supersymmetry of Anti-de Sitter Black Holes

Marco M. Caldarelli, Dietmar Klemm

TL;DR

This work analyzes the supersymmetry of four-dimensional asymptotically AdS dyonic black holes in gauged N=2 supergravity across a range of horizon topologies, including spherical, toroidal, cylindrical, and higher-genus cases, and extends to rotating configurations. By solving the Killing spinor equation and its integrability conditions for static and rotating backgrounds, the authors derive explicit SUSY constraints, construct Killing spinors where possible, and identify novel supersymmetric states tied to horizon topology (notably a nonrotating magnetically charged extremal solution for genus g>1). A key result is that, for KNAdS with spherical horizons, supersymmetry requires vanishing magnetic charge and nonzero rotation in the extremal limit, refining earlier Bogomol’nyi bounds, while for higher-genus horizons there exist truly supersymmetric magnetically charged solitons and their rotating generalizations. The findings illuminate how topology and rotation shape the supersymmetric spectrum of AdS black holes, with potential implications for holography, microscopic entropy, and extensions to higher N supergravities.

Abstract

We examine supersymmetry of four-dimensional asymptotically anti-de Sitter (AdS) dyonic black holes in the context of gauged N=2 supergravity. Our calculations concentrate on black holes with unusual topology and their rotating generalizations, but we also reconsider the spherical rotating dyonic Kerr-Newman-AdS black hole, whose supersymmetry properties have previously been investigated by Kostelecký and Perry within another approach. We find that in the case of spherical, toroidal or cylindrical event horizon topology, the black holes must rotate in order to preserve some supersymmetry; the non-rotating supersymmetric configurations representing naked singularities. However, we show that this is no more true for black holes whose event horizons are Riemann surfaces of genus $g>1$, where we find a nonrotating extremal solitonic black hole carrying magnetic charge and permitting one Killing spinor. For the nonrotating supersymmetric configurations of various topologies, all Killing spinors are explicitly constructed.

Supersymmetry of Anti-de Sitter Black Holes

TL;DR

This work analyzes the supersymmetry of four-dimensional asymptotically AdS dyonic black holes in gauged N=2 supergravity across a range of horizon topologies, including spherical, toroidal, cylindrical, and higher-genus cases, and extends to rotating configurations. By solving the Killing spinor equation and its integrability conditions for static and rotating backgrounds, the authors derive explicit SUSY constraints, construct Killing spinors where possible, and identify novel supersymmetric states tied to horizon topology (notably a nonrotating magnetically charged extremal solution for genus g>1). A key result is that, for KNAdS with spherical horizons, supersymmetry requires vanishing magnetic charge and nonzero rotation in the extremal limit, refining earlier Bogomol’nyi bounds, while for higher-genus horizons there exist truly supersymmetric magnetically charged solitons and their rotating generalizations. The findings illuminate how topology and rotation shape the supersymmetric spectrum of AdS black holes, with potential implications for holography, microscopic entropy, and extensions to higher N supergravities.

Abstract

We examine supersymmetry of four-dimensional asymptotically anti-de Sitter (AdS) dyonic black holes in the context of gauged N=2 supergravity. Our calculations concentrate on black holes with unusual topology and their rotating generalizations, but we also reconsider the spherical rotating dyonic Kerr-Newman-AdS black hole, whose supersymmetry properties have previously been investigated by Kostelecký and Perry within another approach. We find that in the case of spherical, toroidal or cylindrical event horizon topology, the black holes must rotate in order to preserve some supersymmetry; the non-rotating supersymmetric configurations representing naked singularities. However, we show that this is no more true for black holes whose event horizons are Riemann surfaces of genus , where we find a nonrotating extremal solitonic black hole carrying magnetic charge and permitting one Killing spinor. For the nonrotating supersymmetric configurations of various topologies, all Killing spinors are explicitly constructed.

Paper Structure

This paper contains 24 sections, 130 equations.

Table of Contents

  1. Introduction
  2. Anti-de Sitter Black Holes
  3. Nonrotating AdS Black Holes
  4. Kerr-Newman-AdS Black Hole
  5. Rotating Generalization of the Charged $g>1$ Topological Black Holes
  6. Charged Rotating Cylindrical Black Hole
  7. $N=2$ Gauged Supergravity
  8. Supersymmetry of Static Topological Black Holes
  9. Integrability Conditions
  10. Killing Spinors
  11. Genus $g=1$, $V(r) = \frac{r^2}{\ell^2} + \frac{q_e^2}{r^2}$
  12. Genus $g=1$, $V(r) = \frac{z^2}{r^2}$
  13. Genus $g>1$, $V(r) = \left(\frac{r}{\ell} - \frac{\ell}{2r} \right)^2 + \frac{q_e^2}{r^2}$
  14. Genus $g>1$, $V(r) = -1 + \frac{r^2}{\ell^2}$
  15. Supersymmetry of Rotating AdS Black Holes
  16. ...and 9 more sections