We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. 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 AdS 3 in topologically massive gravity, and in string theory. In both cases, the density of states in the 2d field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.arXiv:1210.0539v2 [hep-th]

Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these black holes that lead to a surprisingly simple near horizon symmetry algebra consisting of two affine u(1) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-Hawking entropy of Banados-Teitelboim-Zanelli black holes and "black flower" generalizations. From the near horizon perspective the conformal generators at asymptotic infinity appear as composite operators, which we interpret in the spirit of black hole complementarity. Another remarkable feature of our boundary conditions is that they are singled out by requiring that the whole spectrum is compatible with regularity at the horizon, regardless the value of the global charges like mass or angular momentum. Finally, we address black hole microstates and generalizations to cosmological horizons.Comment: 6p

We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R 1,2 , the flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry non-zero charges under the asymptotic symmetry algebra of R 1,2 , the 3d Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the 2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro algebra, which is isomorphic to BMS3. We study flat holography as a limit of AdS3/CFT2 to semi-classically compute the density of states in the dual, exactly reproducing the bulk entropy in the limit of large charges. Our flat horizons, remnants of the BTZ inner horizons also satisfy a first law of thermodynamics. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers.

Abstract:We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal worldline into a ribbon, and that the anomalous contribution to the CFT entanglement entropy is given by the twist in this ribbon. The entanglement functional may also be interpreted as the worldline action for a spinning particle -that is, an anyon -in three-dimensional curved spacetime. We demonstrate that the minimization of this action results in the Mathisson-PapapetrouDixon equations of motion for a spinning particle in three dimensions. We work out several simple examples and demonstrate agreement with CFT calculations.