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Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity

Chiang-Mei Chen, John E. Wang

TL;DR

The paper extends the Kerr/CFT-like holographic duality to extremal, charged, rotating black holes in five-dimensional minimal supergravity with two angular momenta. By applying the Brown-Henneaux approach to the near-horizon geometry, it derives Virasoro algebras for each angular direction, computes corresponding central charges and Frolov-Thorne temperatures, and verifies that the Cardy entropy matches the Bekenstein-Hawking entropy. It reveals a rotationally induced relation among dual CFTs by treating the two central charges as components of a vector that transforms under angular-plane rotations, and introduces an invariant central charge to describe SUSY BMPV limits. This framework provides a coordinate-independent handle on the dual description and suggests a deeper symmetry among CFTs in higher dimensions, with open questions about a fully unified dual theory.

Abstract

We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with 2 independent angular momenta. The conformal field theory Virasoro algebra, central charge, and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein-Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges leading to an apparent symmetry relating the conformal field theories dual to each black hole. A rotationally invariant central charge, which is proportional to the total angular momentum, is used to discuss the supersymmetric BMPV black hole limits.

Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity

TL;DR

The paper extends the Kerr/CFT-like holographic duality to extremal, charged, rotating black holes in five-dimensional minimal supergravity with two angular momenta. By applying the Brown-Henneaux approach to the near-horizon geometry, it derives Virasoro algebras for each angular direction, computes corresponding central charges and Frolov-Thorne temperatures, and verifies that the Cardy entropy matches the Bekenstein-Hawking entropy. It reveals a rotationally induced relation among dual CFTs by treating the two central charges as components of a vector that transforms under angular-plane rotations, and introduces an invariant central charge to describe SUSY BMPV limits. This framework provides a coordinate-independent handle on the dual description and suggests a deeper symmetry among CFTs in higher dimensions, with open questions about a fully unified dual theory.

Abstract

We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with 2 independent angular momenta. The conformal field theory Virasoro algebra, central charge, and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein-Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges leading to an apparent symmetry relating the conformal field theories dual to each black hole. A rotationally invariant central charge, which is proportional to the total angular momentum, is used to discuss the supersymmetric BMPV black hole limits.

Paper Structure

This paper contains 13 sections, 75 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of the Brown-Henneaux approach
  3. Asymptotic Symmetric Group and Virasoro generators
  4. Central charge
  5. Temperature
  6. Entropy
  7. Black holes in 5D minimal supergravity
  8. General solution
  9. BMPV solution
  10. Central charges as a vector
  11. Invariant central charge and a SUSY condition
  12. Conclusion
  13. Invariance of charge and 5D Kerr String

Figures (3)

  • Figure 1: The plot of the invariant central charge $C^2\propto J^2$ for the choice of parameter $\mu = 2$ and the normalization $\frac{3 \pi}{2 G_5 \hbar} = 1$.
  • Figure 2: The plot of the entropy $S$ for the choice of parameter $\mu = 2$ and the normalization $\frac{\pi^2}{2 G_5 \hbar} = 1$.
  • Figure 3: The plot of the free energy $G$ for the choice of parameter $\mu = 2$ and the normalization $\frac{\pi}{2 G_5 \hbar} = 1$.