Codimension two holography for wedges

TL;DR

This paper introduces a novel codimension two holography framework relating gravity on wedge spacetimes to lower-dimensional CFTs, enabling computation of entanglement entropy and correlation functions, with applications to various dimensions and Lorentzian geometries.

Contribution

It generalizes AdS/CFT to wedge geometries, providing methods to compute holographic quantities and exploring lower-dimensional and Lorentzian cases.

Findings

Holographic entanglement entropy computed by double minimization matches known conformal anomaly results.

Universal quantity analogous to boundary entropy emerges in 2D case.

Wedge holography applied to Lorentzian AdS reproduces CFT entanglement entropy via Wick rotation.

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 space-like 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.