The Kerr/CFT correspondence and its extensions: a comprehensive review

TL;DR

This review analyzes the Kerr/CFT correspondence from first-principles gravity and QFT, showing that extremal horizons possess an asymptotic Virasoro symmetry whose central charge reproduces black hole entropy via a chiral Cardy formula. It extends the framework through gauge-field uplifts, effective field theories, and near-extremal/non-extremal regimes, revealing both exact entropy matches and hidden conformal structures in probe dynamics. The work clarifies when standard AdS/CFT intuition applies and when deformed or warped CFTs are required, highlighting boundary-condition choices, central charges, and the universality of near-horizon dynamics. It also discusses microscopic interpretations of scattering and superradiance, and it identifies substantial open problems, including a fully embedded string-theory dual and a robust non-extremal holographic dictionary. Overall, the paper underscores a compelling, though nuanced, link between black-hole microphysics and two-dimensional conformal symmetry across a broad class of gravitational theories.

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.