Exact microstate counting for dyonic black holes in AdS4 (1608.07294v1)

Abstract: We present a counting of microstates of a class of dyonic BPS black holes in AdS$_4$ which precisely reproduces their Bekenstein-Hawking entropy. The counting is performed in the dual boundary description, that provides a non-perturbative definition of quantum gravity, in terms of a twisted and mass-deformed ABJM theory. We evaluate its twisted index and propose an extremization principle to extract the entropy, which reproduces the attractor mechanism in gauged supergravity.

• The paper introduces a method using the twisted index of a mass-deformed ABJM theory to non-perturbatively count the exact microstates of dyonic BPS black holes in AdS4.
• This microstate counting is shown to precisely match the Bekenstein-Hawking entropy of these black holes, providing a crucial validation of the AdS/CFT correspondence in this context.
• The counting is achieved through an extremization principle involving complex chemical potentials, which is equivalent to the attractor mechanism in gauged supergravity.

Exact Microstate Counting for Dyonic Black Holes in AdS${}_4$

The research paper examines the intricate topic of black hole microstate counting within the field of AdS${}_4$. Notably, it proposes a method for evaluating the microstates of a certain class of dyonic BPS black holes situated in AdS${}_4$, and demonstrates that this counting accurately correlates with the Bekenstein-Hawking entropy. This is accomplished through calculations details from the dual boundary description, notably a mass-deformed ABJM theory. By leveraging its twisted index, the authors introduce an extremization principle to determine the black hole entropy, reflecting the attractor mechanism present in gauged supergravity.

In the context of string theory, supersymmetric black holes offer valuable insights for understanding quantum gravity. A major question in this field revolves around the origins of black hole entropy, which is statistically anticipated to enumerate the degenerate black hole configurations. Notably, while string theory has adequately explained the entropy of some asymptotically flat black holes, the understanding of those asymptotically approaching the AdS environments, particularly in dimensions equaling or exceeding four, remains limited. The advent of the AdS/CFT correspondence provides a robust, non-perturbative framework for exploring quantum gravity within these settings by employing dual boundary quantum field theories. In this proposed method, a twisted version of ABJM theory facilitates the non-perturbative computation of quantum entropies for the dyonic BPS black holes in AdS${}_4$, which successfully aligns with the known Bekenstein-Hawking entropy.

The authors extend this work to show that the entropy of BPS black holes characterized by magnetic and electric charges, and those asymptotic to AdS${}_4 \times S^7$, can be deduced through an extremization principle. This involves extremizing the expression: $I = \log Z(u_a) - i \sum\nolimits_a u_a q_a$ with respect to certain complex chemical potentials $u_a$. Here, $Z(u_a)$ refers to the topologically twisted index of the ABJM theory, inherently dependent on the magnetic charges. This extremization is found to be equivalent to the attractor mechanism in gauged supergravity, supporting the hypothesis that the extremization leads to selecting the exact R-symmetry of the superconformal quantum mechanics associated with the AdS${}_2$ horizon region.

The work explores specifics involving the STU model, a four-dimensional $N=2$ gauged supergravity model with three vector multiplets. The solutions examined can be embedded in M-theory, helping to elucidate the near-horizon geometry characterized by a Riemann surface. These configurations offer pathways for associating BPS black holes with certain symmetries and vector fields akin to those in four-dimensional gauged supergravity.

Moreover, the utilization of the AdS/CFT correspondence alongside advances in calculating the supersymmetric localization of the twisted index provides a framework for addressing the non-perturbative aspects of this quantum gravity calculation. By establishing a bridge between ABJM theory and the dual boundary QFT, the authors offer a non-trivial match with the supergravity solutions verified via the established entropy formula, thus reinforcing the theoretical underpinnings of their approach.

This research carries significant implications, both theoretically and practically, in advancing the understanding of quantum entropies within the framework of the AdS/CFT correspondence and gauged supergravity. It holds potential for future developments in AI and theoretical physic modeling, offering new pathways for exploring quantum gravity's fundamental aspects through dual theories and their non-perturbative techniques.