Quantum black holes: supersymmetry and exact results (2502.15360v1)

Abstract: The explanation of black hole entropy as statistical entropy is one of the big successes of string theory. In this article we review recent progress in this subject, focussing on understanding quantum effects on black hole entropy. Supersymmetry plays a key role in these developments and leads to prototype systems where we can discuss quantum effects to great precision. Our discussion has two strands, both of which involve the gravitational path integral that calculates the supersymmetric index. In the first strand we discuss supersymmetric black holes in the microcanonical ensemble, which are decoupled from the environment and can be treated as independent quantum systems. Using methods of supersymmetric localization one can arrive at the integer quantum degeneracies of such systems purely in terms of the gravitational variables. In the second strand we consider grand-canonical ensembles in gravity in which black holes arise as a finite-action excitation in asymptotically flat or Anti de Sitter space. In this context we discuss the saddle-points of the gravitational index, and how they reproduce the black hole action and entropy that agree with the index of the holographic superconformal field theory even beyond the leading order in the semiclassical approximation. Finally we discuss how the gravitational index informs us about the detailed structure of the non-perturbative sum over saddle points and the resulting phases of the theory. Throughout, we try to highlight the central role played by the methods as well as foundational concepts of supergravity in driving these developments.

Exploring Quantum Black Holes: Supersymmetry and Precise Outcomes

The paper "Quantum black holes: supersymmetry and exact results" provides a comprehensive review of the advancements in understanding quantum effects on black hole (BH) entropy, a haLLMark achievement of string theory. The authors, Cassani and Murthy, explore the intricate relationship between quantum mechanics, gravity, and thermodynamics through the lens of string theory and supersymmetry. The discussion is anchored in two main areas: the microcanonical ensemble of quantum gravitational systems and the grand-canonical ensemble examining BHs within gravitational thermodynamics.

A principal achievement of string theory is the microscopic interpretation of BH entropy, as pioneered by Strominger and Vafa. They demonstrated that the Bekenstein-Hawking entropy formula, a cornerstone of BH physics, corresponds to the statistical entropy of D-brane states, invariant under string coupling changes due to supersymmetry.

The paper examines quantum entropy through the framework of supersymmetry, enabling a profound understanding of BHs as isolated quantum systems. Here, an exact combing of microscopic quantum states provides a richer expression of BH entropy beyond the semiclassical Bekenstein-Hawking formula. In this context, the AdS$_2$/CFT$_1$ correspondence offers a potent analogy, where successful calculations hinge on robust techniques like supersymmetric localization—a method that refines path integrals by honing onto supersymmetric field configurations.

A crucial advance discussed in the paper is the computation of quantum corrections, reflected in the focus on the gravitational path integral within AdS space, incorporating grand-canonical ensembles. This approach models BHs as quantitative changes in finite-action states in AdS/CFT settings. The index used here transcends leading semiclassical approximations, capturing black hole action and entropy, fostering a bridge between gravitational solutions and holographic field theory indices. This dual perspective gives researchers a tool to probe nonperturbative dynamics in quantum spacetime.

Through supersymmetry, BHs are analyzed in regimes beyond their semiclassical portrayals. The research confirms that complex solutions reflecting non-extremal, finite-temperature conditions provide a rich thermodynamic picture even when traditional methods fall short. These complex supersymmetric solutions can reveal more about quantum gravitational systems when examined through a framework envisioning BHs as the sum of micro-states reflected in the quantum field theories.

The implications of these findings stretch into various domains, including quantum information theory, where the exact entropies and indices from supergravity models serve as a touchstone for the emerging landscapes of quantum gravity theories, revealing the modularity and integrity of the universe's fabric in both extreme and subtle quantum regimes.

The advancements in understanding BHs from a quantum perspective provide essential insights into how the universe computes information and reveals the nature of gravitational interactions at both microscopic and macroscopic scales. As the field continues to evolve, this synergy between black hole thermodynamics and quantum field theories will undoubtedly remain a central pivot in theoretical physics.