The Kerr/CFT correspondence and its extensions

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.

Entanglement entropy in flat holography

“…Now we consider the BMSFT on the plane with zero temperature. In this case the symmetry generators of BMS 3 are 16) where the n = −1, 0, 1 part form a subalgebra, and generate the global symmetries. By matching the general form of Killing vectors in (4.9), one can easily see that…”

“…However, if we take r → ∞ in (6.6), N + ∩ N − intersects with the boundary at (u, φ) = (−π, −∞) and (π, −∞). The reason is that the boundary end points ∂A 1,2 are the fixed points of k t but not the fixed points of k bulk 16) and thus N + ∩ N − will never go through ∂A 1,2 . It is interesting that the orbits of ∂A 1,2 under the bulk modular flow k bulk t are just γ ± .…”

“…To understand the generality, it is important to extend the great success of holography beyond the context of AdS/CFT. Progresses for non-AlAdS holography includes dS/CFT correspondence [6,7], the Shrödinger or Lifshitz spacetime/non-relativistic field theory duality [8][9][10][11], the Kerr/CFT correspondence [12][13][14][15][16], the WAdS/CFT [17] or WAdS/WCFT [18,19] correspondence, and illuminating results toward flat holography in four dimensions [20][21][22][23] and three dimensions [24][25][26][27]. A general item in the dictionary of holography is that the asymptotic symmetry for the gravitational theory in the bulk agrees with the symmetry of the dual field theory, if the later exists.…”

Conceptual Aspects of Gauge/Gravity Duality

“…these macroscopic quantities vary slowly over the fluid. 29 The hydrodynamic approximation can be improved by including terms with more and more derivatives of u μ ; in other words, hydrodynamics is a perturbative expansion in the number of derivatives of u μ . At each level in derivatives, all the possible terms that one can construct with n derivatives introduce new constants.…”

Warped AdS3 black holes in higher derivative gravity theories

“…This includes for instance dS/CFT [41], AdS/Condensed Matter Theory [42,43], Non-relativistic Schrödinger and Lifshitz Holography [44], Hyperscaling geometries [45], Flat Space Holography [46] and Kerr/CFT [25,47] (references are by no means meant to be extensive, and point most of the time at reviews on the subjects).…”