An Exact Construction of Codimension two Holography

TL;DR

This paper constructs an exact gravitational solution framework for wedge holography, proving its equivalence to AdS/CFT in vacuum Einstein gravity, and extends the approach to dS/CFT and flat space holography.

Contribution

It provides an exact construction linking wedge holography to AdS/CFT, establishing their equivalence, and explores extensions to other holographic dualities.

Findings

Proves wedge holography is equivalent to AdS/CFT for vacuum Einstein gravity.

Derives holographic Weyl anomaly, entanglement entropy, and correlation functions.

Unifies AdS/CFT, dS/CFT, and flat space holography within a codimension two framework.

Abstract

Recently, a codimension two holography called wedge holography is proposed as a generalization of AdS/CFT. It is conjectured that a gravitational theory in $d+1$ dimensional wedge spacetime is dual to a $d-1$ dimensional CFT on the corner of the wedge. In this paper, we give an exact construction of the gravitational solutions for wedge holography from the ones in AdS/CFT. By applying this construction, we prove the equivalence between wedge holography and AdS/CFT for vacuum Einstein gravity, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the same for the two theories. The equivalence to AdS/CFT can be regarded as a "proof" of wedge holography in a certain sense. As an application of this powerful equivalence, we derive easily the holographic Weyl anomaly, holographic Entanglement/R\'enyi entropy and correlation functions for wedge holography. Besides, we discuss the general solutions of wedge holography and argue that they correspond to the AdS/CFT with suitable matter fields. Interestingly, we notice that the intrinsic Ricci scalar on the brane is always a constant, which depends on the tension. Finally, we generalize the discussions to dS/CFT and flat space holography. Remarkably, we find that AdS/CFT, dS/CFT and flat space holography can be unified in the framework of codimension two holography in asymptotically AdS. Different dualities are distinguished by different types of spacetimes on the brane.