4.4 Article

An exact construction of codimension two holography

Journal

JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -

Publisher

SPRINGER
DOI: 10.1007/JHEP01(2021)150

Keywords

AdS-CFT Correspondence; Classical Theories of Gravity

Funding

  1. NSFC [11905297]
  2. Guangdong Basic and Applied Basic Research Foundation [2020A1515010900]

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In this paper, a codimension two holography called wedge holography is introduced as a generalization of AdS/CFT, with exact construction of gravitational solutions provided. The equivalence between wedge holography and AdS/CFT for vacuum Einstein gravity is proven, leading to insights on holographic Weyl anomaly, Entanglement/Renyi entropy and correlation functions. The study also extends to dS/CFT and flat space holography, revealing a unification of different holographic models in the framework of codimension two holography in asymptotically AdS.
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/Renyi 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.

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