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.
Highlights
The anti-de Sitter space (AdS)=conformal field theory (CFT) correspondence plays an important role in our modern understanding of quantum gravity [1,2,3]
By taking the zero-volume limit of AdS/BCFT, i.e., M → 0, we are left with the edge mods on Σ, and we obtain the wedge holography as shown in Fig. 1, which can be regarded as a holographic dual of edge modes as we have argued above
II, we formulate the cone holography and prove that it is equivalent to AdS=CFT with Einstein gravity for a novel class of solutions
Summary
The AdS=CFT correspondence plays an important role in our modern understanding of quantum gravity [1,2,3]. By taking the zero-volume limit of AdS/BCFT, i.e., M → 0, we are left with the edge mods on Σ, and we obtain the wedge holography as shown in Fig. 1 (right), which can be regarded as a holographic dual of edge modes as we have argued above. The two kinds of edge modes both live on the 2D defect D effectively in the zero-volume limit This is the case for general d and m. The gravity theory in the (d þ 1)-dimensional conical spacetime C is dual to the edge modes (CFT) on the (d-m)-dimensional defect D We call this novel holography cone holography or codimension-n holography, where n 1⁄4 m þ 1.
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