Warped Conformal Field Theory

TL;DR

Warped Conformal Field Theories (WCFTs) are 2d field theories with chiral scaling symmetry whose local symmetry algebra is a Virasoro algebra plus a U(1) current. The authors derive a warped modular invariance that yields a Cardy-like universal entropy formula, applicable even when full conformal symmetry is absent. They test the framework holographically in warped AdS3 spacetimes within topologically massive gravity and in string-theory constructions, showing WCFT entropy matches Bekenstein-Hawking entropy for warped black holes. The work also analyzes nonlocal deformations and alternative ensembles, revealing a broader holographic relevance for non-AdS spacetimes and providing insight relevant to Kerr/CFT and higher-spin contexts.

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.