Codimension-two holography for wedges

Abstract

We propose a codimension-two holography between a gravitational theory on a d+1 dimensional wedge spacetime and a d-1 dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity (d=3), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reproduces the known result expected from the holographic conformal anomaly. We also discuss a lower dimensional example (d=2) and find that a universal quantity naturally arises from gravity, which is analogous to the boundary entropy. Moreover, we consider a gravity on a wedge region in Lorentzian AdS, which is expected to be dual to a CFT with a spacelike boundary. We formulate this new holography and compute the holographic entanglement entropy via a Wick rotation of the AdS/BCFT construction. Via a conformal map, this wedge spacetime is mapped into a geometry where a bubble-of-nothing expands under time evolution. We reproduce the holographic entanglement entropy for this gravity dual via CFT calculations.