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 two-dimensional 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 two-dimensional field theory with chiral scaling. We consider two examples: black holes in warped ${\mathrm{AdS}}_{3}$ in topologically massive gravity and in string theory. In both cases, the density of states in the two-dimensional field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.