Codimension two holography for wedges

TL;DR

The paper introduces wedge holography, a codimension-two duality linking gravity on a wedge W_{d+1} to a d−1 dimensional CFT on Σ, realized as a limit of AdS/BCFT and brane-world holography. It develops a general framework in arbitrary dimensions, derives a double-minimization prescription for holographic entanglement entropy, and analyzes the spectrum of bulk fields via dimensional reduction, confirming consistency with conformal data. The authors provide detailed results for d=3 (AdS_4/CFT_2) and d=2 (AdS_3/CFT_1), including the conformal anomaly, entanglement entropy, and the role of boundary entropy, and explore Lorentzian wedges with space-like boundaries and bubble nucleations. Overall, wedge holography offers a coherent, testable extension of holography to higher codimensions with rich connections to BCFT, edge modes, and deformations such as BTZ and de Sitter-like configurations.

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.

Figures (17)

• Figure 1: A sketch of wedge holography.
• Figure 2: A basic setup of wedge holography with UV regularization.
• Figure 3: A sketch of derivation of wedge holography from AdS/BCFT. The left picture describes the gravity dual of a CFT on a semi-infinite plane. The right one shows the gravity dual of a CFT on an interval.
• Figure 4: A sketch of compactified setup of wedge holography.
• Figure 5: A sketch of calculation of holographic entanglement entropy in codimension two holography (left) and in AdS/BCFT (right).