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Gravitational Cardy Limit and AdS Black Hole Entropy

Marina David, Jun Nian, Leopoldo A. Pando Zayas

TL;DR

This work establishes a universal gravitational Cardy limit that mirrors the field theory Cardy-like scaling in rotating, charged AdS black holes across dimensions. By pairing a near-horizon Bardeen-Horowitz limit with a dimension-dependent gravitational Cardy limit, the authors reveal a reduced AdS3 structure whose Virasoro symmetries yield entropy via Cardy formulas that match the Bekenstein-Hawking results and boundary CFT predictions. The results demonstrate a dimension-spanning universality: AdS5, AdS4, AdS6, and AdS7 black holes each admit a near-horizon AdS3/CFT2 description whose central charge and Frolov-Thorne temperature reproduce the correct entropy, in agreement with dual field theories including N=4 SYM, ABJM, and the 6d (2,0) theory. The analysis provides a low-energy, symmetry-based microscopic account of AdS black hole entropy and highlights a shared AdS3-sector underlying diverse holographic duals. Future directions include understanding the emergent NH CFT2 in the full CFT_d, extending to near-extremal cases, and incorporating higher-derivative corrections.

Abstract

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta, and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS$_{4, 5, 6, 7}$ BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.

Gravitational Cardy Limit and AdS Black Hole Entropy

TL;DR

This work establishes a universal gravitational Cardy limit that mirrors the field theory Cardy-like scaling in rotating, charged AdS black holes across dimensions. By pairing a near-horizon Bardeen-Horowitz limit with a dimension-dependent gravitational Cardy limit, the authors reveal a reduced AdS3 structure whose Virasoro symmetries yield entropy via Cardy formulas that match the Bekenstein-Hawking results and boundary CFT predictions. The results demonstrate a dimension-spanning universality: AdS5, AdS4, AdS6, and AdS7 black holes each admit a near-horizon AdS3/CFT2 description whose central charge and Frolov-Thorne temperature reproduce the correct entropy, in agreement with dual field theories including N=4 SYM, ABJM, and the 6d (2,0) theory. The analysis provides a low-energy, symmetry-based microscopic account of AdS black hole entropy and highlights a shared AdS3-sector underlying diverse holographic duals. Future directions include understanding the emergent NH CFT2 in the full CFT_d, extending to near-extremal cases, and incorporating higher-derivative corrections.

Abstract

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta, and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.

Paper Structure

This paper contains 38 sections, 229 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Asymptotically AdS$_5$ Black Holes
  3. AdS$_5$ Black Hole Solution
  4. Gravitational Cardy Limit
  5. Black Hole Solution in the Near-Horizon + Gravitational Cardy Limit
  6. Black Hole Entropy from Cardy Formula
  7. Comparison with Results from Boundary CFT
  8. Asymptotically AdS$_4$ Black Holes
  9. AdS$_4$ Black Hole Solution
  10. Gravitational Cardy Limit
  11. Black Hole Solution in the Near-Horizon + Gravitational Cardy Limit
  12. Black Hole Entropy from Cardy Formula
  13. Comparison with Results from Boundary CFT
  14. Asymptotically AdS$_7$ Black Holes
  15. A Special Case
  16. ...and 23 more sections

Figures (1)

  • Figure 1: The Gravitational Cardy limit plays a role in the broader picture of the study of AdS black holes, giving us a near-horizon AdS$_3$ geometry, similar to that of the extremal vanishing horizon limit. The entropy can be computed in three separate regimes ($S_{BH}^{(i)}$), and are all found to be equal.