CFT Duals for Extreme Black Holes (0811.4393v2)

Abstract: It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.

• The paper extends the Kerr/CFT correspondence by proposing a dual CFT description for extremal Kerr-Newman-AdS-dS black holes based on near-horizon Virasoro symmetries.
• It rigorously derives the central charge and temperature using semiclassical methods, ensuring that the Cardy formula accurately reproduces the macroscopic Bekenstein-Hawking entropy.
• The study explores alternative dual descriptions for non-rotating cases and generalizes the framework to higher-dimensional black holes, offering deeper insights into quantum gravity.

Overview of "CFT Duals for Extreme Black Holes"

The paper "CFT Duals for Extreme Black Holes" advances the notion that extremal black holes in four dimensions, specifically the Kerr-Newman-AdS-dS black holes, have holographic duals in the form of two-dimensional conformal field theories (CFTs). This research builds upon the known Kerr/CFT correspondence, extending it to a broader class of black hole spacetimes.

Key Concepts and Contributions

1. Holographic Duality and Virasoro Algebra: The authors conjecture that the asymptotic symmetries of the near-horizon region of extremal black holes can be captured through a dual CFT description. The asymptotic symmetries, expressed by the Virasoro algebra, are pivotal, providing insights into the microscopic composition of black holes.
2. Central Charge and Temperature Derivation: The central charge and temperature of the dual CFT are derived using semiclassical formulae. These quantities depend on several parameters, such as the cosmological constant, Newton's constant, black hole charges, and spin. Such rigorous derivation ensures the CFT's microscopic entropy aligns with the macroscopic Bekenstein-Hawking area law via the application of the Cardy formula.
3. Cardy Formula Application: The successful application of the Cardy formula to reproduce the Bekenstein-Hawking entropy is a strong supportive argument for the duality conjecture. This comparable entropy identification is robust for Kerr-Newman-AdS-dS black holes but encounters regularity issues in the Reissner-Nordstrom limit as angular momentum vanishes.
4. Alternative Dual Descriptions: In cases like the extremal Reissner-Nordstrom black hole, where the spin is zero, the paper proposes an alternative CFT description that includes promoting the global U(1) gauge symmetry to a Virasoro algebra, which still correctly reproduces the black hole entropy.
5. Generalization to Higher Dimensions: The research explores possible generalizations of the Kerr/CFT correspondence to encompass higher-dimensional black holes and more complex geometries, including the use of a 5-dimensional perspective where applicable.

Implications and Future Directions

The findings have both theoretical and practical implications in the field of high-energy theoretical physics, particularly in understanding the microstates of black holes. The proposed CFT dual models offer a pathway to explore quantum gravity effects in black hole physics.

Practical implications may eventually lead to insights into quantum gravity theories and might influence the development of a consistent theory of quantum gravity. The implications for string theory are significant, as the results mirror similar structures encountered in string-theoretical black holes, hinting at deeper unifying principles.

Future research can potentially explore:

• Extending the Kerr/CFT correspondence to other exotic black hole solutions beyond four dimensions.
• Investigation of the robustness of the Virasoro algebra under different physical conditions and within other theoretical frameworks.
• Exploring more sophisticated dual models that capture additional physical phenomena, such as higher derivative corrections.

Conclusion

Through detailed analytic techniques, the authors deepen the understanding of how holographic principles might illuminate the microstructure of black holes. The congruence between the macroscopic and microscopic entropic measures presents a compelling case for the validity of CFT duals concerning extreme black holes, further enriching the discourse on the nature of black holes and their entropic characteristics. The paper stands as a testament to the intricate connections between general relativity, quantum mechanics, and high-energy physics.