Codimension-n Holography for Cones

TL;DR

This paper introduces cone holography, a new form of holographic duality relating gravitational theories in conical spacetimes to defect conformal field theories, supported by various consistency checks and comparisons.

Contribution

It proposes cone holography as a novel generalization of wedge holography, establishing its equivalence to AdS/CFT in certain cases and exploring its properties and applications.

Findings

Good agreement between holographic and CFT calculations of Weyl anomaly and entanglement entropy.

The c-theorem is satisfied within cone holography.

The mass spectrum on the brane varies with tension, becoming more continuous as tension increases.

Abstract

We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography can be obtained by taking the zero-volume limit of holographic defect CFT. Remarkably, it can be regarded as a holographic dual of the edge modes on the defects. For one class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the same for the two theories. In general, cone holography and AdS/CFT are different due to the infinite towers of massive Kaluza-Klein modes on the branes. We test cone holography by studying Weyl anomaly, Entanglement/R\'enyi entropy and correlation functions, and find good agreements between the holographic and the CFT results. In particular, the c-theorem is obeyed by cone holography. These are strong supports for our proposal. We discuss two kinds of boundary conditions, the mixed boundary condition and Neumann boundary condition, and find that they both define a consistent theory of cone holography. We also analyze the mass spectrum on the brane and find that the larger the tension is, the more continuous the mass spectrum is. The cone holography can be regarded as a generalization of the wedge holography, and it is closely related to the defect CFT, entanglement/R\'enyi entropy and AdS/BCFT(dCFT). Thus it is expected to have a wide range of applications.