Warped conformal field theory

Abstract

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]

The Brown-York mass of black holes in Warped Anti-de Sitter space

“…That is, the asymptotic isometry group in WAdS 3 spaces certainly differs from the two-dimensional conformal group; nevertheless, it has been shown in [11] that, under certain circumstances, the symmetry results powerful enough to constrain the dual theory and extract relevant information from it. The holographic description of WAdS 3 black hole thermodynamics carried out in [11] is a notable realization of this idea.…”

“…This defines the energy density; see [28,40] for discussions. From (11) we see that the line element ds in the case we are interested in is simply ds = ρdϕ.…”

“…In the case of the mass, the components of this vector are ξ i = N t u i , where the lapse function N t (r) in (11). This defines the energy density; see [28,40] for discussions.…”

“…[1], and it was further studied in Refs. [2][3][4][5][6][7][8][9][10][11]. This represents one of the most appealing attempts to generalize holography to non-AdS spaces, and this is because WAdS spaces appear in several contexts.…”

Comments on Rényi entropy in AdS3/CFT2

“…The results in section 6 do not apply to warped AdS, nor to warped CFTs [76]: we do not yet understand warped CFT conformal blocks, nor is warped AdS a quotient of ordinary AdS. Some work on entanglement entropy in…”