The Kerr/CFT correspondence and its extensions: a comprehensive review (1203.3561v4)

Abstract: We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy's formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy's formula. We follow an effective field theory approach and consider the Kerr-Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.

• The paper reveals that the asymptotic Virasoro symmetry in near-horizon geometries reproduces black hole entropy via Cardy’s formula.
• It extends the correspondence to Kerr-Newman black holes by incorporating dual U(1) symmetries and aligning thermodynamic potentials.
• Hidden conformal symmetries in low-energy regimes indicate broader holographic applications beyond extremal solutions.

An Academic Overview: "The Kerr/CFT Correspondence and its Extensions"

The paper "The Kerr/CFT Correspondence and its Extensions" offers a comprehensive exploration of the Kerr/CFT correspondence and seeks to extend its theoretical framework utilizing gravity and quantum field theory tools. This paper revolves around the intricate relationship between the physics of extremal black holes and two-dimensional conformal field theories (CFTs).

Background and Motivation

Central to the discussion are extremal spinning and charged black holes, which possess unique thermodynamic properties despite their zero temperature. A significant challenge remains to fully understand the microscopic origins of these properties, which is essential for a theory of quantum gravity. The Kerr/CFT correspondence attempts to illuminate these microstates using holographic principles, which posit that gravitational systems can be equivalently described by a lower-dimensional non-gravitational theory.

Main Results

Symmetry Analysis and Entropy Matching

1. Asymptotic Virasoro Symmetry: The paper explores extremal black holes' near-horizon geometries, revealing an asymptotic Virasoro symmetry. The central charge associated with this algebra is pivotal in matching the Bekenstein-Hawking entropy of the black holes using Cardy's formula, a keystone result first highlighted for the Kerr black hole.
2. Interplay with Conformal Field Theories:
   • Extremal Black Holes: The entropy of extremal Kerr and Reissner–Nordström black holes aligns with Cardy's formula for chiral halves of CFTs, despite being outside Cardy’s usual applicability range.
   • Extensions to Kerr–Newman Black Holes: The authors extend these arguments to Kerr–Newman black holes, proposing that both an axial and an electromagnetic symmetry can give rise to Virasoro algebras, underpinning the holographic interpretation.
3. Thermodynamic Potentials: The paper defines critical thermodynamic potentials at extremality, derived from non-extremal counterparts, providing deeper insights into black holes' statistical mechanics.

Probing Near-Extremal Dynamics

Exploring perturbations around near-extremal black holes, the authors reproduce scattering amplitudes using the structure of CFT correlation functions. This non-trivial match supports the notion that remnants of CFT dynamics prevail close to extremality.

Hidden Conformal Symmetries

Interestingly, the research identifies "hidden" conformal symmetries in the low-energy, long-wavelength regime of certain non-extremal black hole backgrounds. This implies a broader applicability of Kerr/CFT-like correspondences beyond extremal solutions under restricted conditions.

Implications and Future Directions

The implications of this research are profound, suggesting that black hole microstates, even those for realistic astrophysical black holes, might be encapsulated within a CFT framework. The extension of Kerr/CFT to incorporate multiple U(1) symmetries enriches its potential application across varied black hole solutions.

Theoretically, the establishment of CFT duals for low-energy black hole dynamics paves pathways to more robust quantum gravity formulations, where black holes are no longer singular endpoints but part of an array of holographically equivalent descriptions. Future work will likely explore understanding these symmetries' deformation, incorporating higher-dimensional theories, and further exploring the bridge between macroscopic and microscopic descriptions of black holes.

Conclusion

The paper establishes critical relationships between the rich symmetry structures of extremal and near-extremal black holes and CFTs. While many open questions remain regarding constructing explicit CFT duals and their full-fledged extensions, this work stands as a significant step towards bridging the gap between gravity and quantum field theories in describing black hole microphysics.