Large AdS black holes from QFT (1810.12067v3)

Abstract: We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$ at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large $N$. Our result is derived using free QFT analysis, and also a background field method on $S^3$. The index sets a lower bound on the entropy. It saturates the Bekenstein-Hawking entropy of known supersymmetric AdS$_5$ black holes, thus accounting for their microstates. We further analyze the so-called Macdonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS$_7$ black holes, using background field method on $S^5$ and 't Hooft anomalies.

• The paper derives macroscopic entropy for large supersymmetric AdS black holes from QFT indices, matching the Bekenstein-Hawking entropy for AdS5 black holes.
• It successfully counts microstates for AdS5 black holes by employing a generalized Cardy limit within $\mathcal{N}=4$ Yang-Mills theory on S$^3$, extending previous methods.
• The study explores the existence of small and potentially new hairy black holes using techniques like the Macdonald index and analyzes large AdS7 black holes via anomalies on S$^5$.

Overview of "Large AdS Black Holes from QFT"

This paper explores the derivation of the entropy of large AdS black holes from the perspective of Quantum Field Theory (QFT), particularly focusing on supersymmetric black holes in AdS$_5$ and AdS$_7$ spaces. It presents a detailed paper of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$, examining the indices at large angular momenta and connecting these results to the microstate counting of AdS black holes.

In the first part, the authors use a generalized Cardy limit to reveal a macroscopic entropy at large $N$, derived via free QFT analysis and a background field method on $S^3$. The index effectively acts as a lower bound on the entropy and is shown to equate with the Bekenstein-Hawking entropy of known supersymmetric AdS$_5$ black holes, thereby accounting for their microstates. Extending their previous work, they apply techniques reminiscent of the Macdonald index to explore the existence of small and potentially new hairy black holes.

In the final sections, the paper transitions to large supersymmetric AdS$_7$ black holes, employing background field methods on $S^5$ and analyzing 't Hooft anomalies. The derivations suggest new directions in the exploration of the physical and theoretical implications of these findings.

Key Results and Claims

• Macroscopic Entropy Discovery: The paper demonstrates a macroscopic entropy at large $N$, which in turn saturates the Bekenstein-Hawking entropy for known supersymmetric AdS$_5$ black holes. This pivotal result is achieved through a refined use of the Cardy limit within the indices of $\mathcal{N}=4$ Yang-Mills theory.
• Microstate Counting: The authors successfully perform microstate counting for AdS$_5$ black holes by implementing the generalized Cardy limit and correlating it with QFT indices.
• New Black Hole Constructs: Using the Macdonald index as a basis, the paper explores small black holes and hints at the existence of potential new black hole structures analogous to hairy black holes. This includes insights into large AdS$_7$ black holes using anomalies on $S^5$.

Implications and Speculations

The paper offers rich implications for the understanding of AdS/CFT correspondence and the nature of quantum microstates in black hole physics. By leveraging QFT methods to account for supersymmetric black hole microstates, the authors contribute to bridging the gap between theoretical predictions and gravitational phenomena.

On the theoretical side, their findings suggest potential expansions toward understanding BPS black holes in various AdS dimensions beyond the scope of supersymmetry alone. Practically, these insights might guide further research in exploring non-trivial black holes, such as hairy black holes, and understanding how these entities manifest through quantum state degeneracies.

Future Directions

The work opens avenues for broader exploration into AdS$_4$ and AdS$_6$ black holes using similar methodologies, expanding the theoretical framework to encompass different supersymmetric configurations and gauge theories. Additionally, these findings highlight the potential for further refining QFT approaches to identify new black hole entities and corroborate known gravitational models with quantum predictions.

By asserting bold yet rigorous arguments through mathematical derivations and substantiated theoretical models, the authors offer a foundation upon which subsequent research can be built. This includes exploring deeper into the large $N$ landscape, potentially leading to discoveries that challenge current understandings and assumptions within high-energy theoretical physics.