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Heat Kernel Expansion and Extremal KerrNewmann Black Hole Entropy in EinsteinMaxwell Theory
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Conformal symmetry for black holes in four dimensions and irrelevant deformations, arXiv:1210.7695 [hepth
"... Abstract: It has been argued several times in the past that the structure of the entropy formula for general nonextremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry. A recent implementation of this idea, carried out by Cvetič an ..."
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Abstract: It has been argued several times in the past that the structure of the entropy formula for general nonextremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry. A recent implementation of this idea, carried out by Cvetič and Larsen, involves the replacement of a conformal factor in the original geometry by an alternative conformal factor in such a way that the nearhorizon behavior and thermodynamic properties of the black hole remain unchanged, while only the asymptotics or "environment" of the geometry are modified. The solution thus obtained, dubbed "subtracted geometry", uplifts to an asymptotically AdS 3 ×S 2 black hole in five dimensions, and an AdS/CFT interpretation is then possible. Building on this intuition we show that, at least in the static case, the replacement of the conformal factor can be implemented dynamically by means of an interpolating flow which we construct explicitly. Furthermore, we show that this flow can be understood as the effect of irrelevant perturbations from the point of view of the dual twodimensional CFT, and we identify the quantum numbers of the operators responsible for the flow. This allows us to address quantitatively the validity of CFT computations for these asymptotically flat black holes and provides a framework to systematically compute corrections to the CFT results.
Warped Conformal Field Theory
"... We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on rightmovers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d conformal group, but in some respects is equally powerful i ..."
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We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on rightmovers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d conformal group, but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near horizon geometry of any extremal black hole are identical to those of a 2d field theory with chiral scaling. We consider two examples: black holes in warped AdS3 in topologically massive gravity, and in string theory. In both cases, the density of states in the 2d field theory reproduces the BekensteinHawking entropy of black holes in the gravity theory. ar X iv
Two Virasoro symmetries in stringy warped AdS3
, 2014
"... We study threedimensional consistent truncations of type IIB supergravity which admit warped AdS3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the nondynamical subsectors, equals the symplectic form ..."
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We study threedimensional consistent truncations of type IIB supergravity which admit warped AdS3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the nondynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS3. Consequently, for each consistent choice of boundary conditions in AdS3, we can define a consistent phase space in warped AdS3 with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS3; two different types of Virasoro × KačMoody symmetries are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearized) phase space. This implies that, at least at semiclassical level, consistent theories of gravity in warped AdS3 are described by a twodimensional conformal field theory, as long as stability is not an issue.