An exact construction of codimension two holography

• Main Author: Rong-Xin Miao
• Format: Article
• Language: English
• Published: SpringerOpen 2021-01-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Classical Theories of Gravity
• Online Access: https://doi.org/10.1007/JHEP01(2021)150

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.