An Exact Construction of Codimension two Holography

TL;DR

The paper formulates an exact map from AdS_d/CFT_{d-1} vacuum Einstein solutions to wedge holography AdSW_{d+1}/CFT_{d-1}, proving a classical equivalence of the gravitational actions for a novel solution class. This equivalence enables direct derivations of holographic Weyl anomaly, entanglement/Rényi entropy, and stress-tensor correlators within wedge holography, matching the expected AdS/CFT results. The authors then explore more general brane spacetimes, showing the brane Ricci scalar is constant and that brane matter (often CFT-like) can arise, suggesting wedge holography with matter fields corresponds to AdS/CFT with brane matter. They extend the framework to dS/CFT and flat space holography, unifying AdS/CFT, dS/CFT, and flat space holography under codimension-two holography, and outline open problems such as including matter, black holes, and higher-derivative corrections.

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/Rényi 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.

Figures (3)

• Figure 1: (left) Geometry of wedge holography; (right) Wedge holography from AdS/BCFT
• Figure 2: UV Planck brane (blue) and IR Planck brane (red). The smaller the tension $T=(d-1) \tanh\rho$ is, the deeper the brane bends into the bulk (IR). Thus $\rho$ decreases under RG flows.
• Figure 3: Geometry of cosmic brane. The red line denotes a subsystem A on $\Sigma$, and the gray surface denotes the cosmic brane ending on the end-of-world branes $Q_1$ and $Q_2$. Note that the intersection of cosmic brane and $\Sigma$ is $\partial A$.