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This talk is based on [1].

As the most well-established example of holographic principle, the AdS/CFT correspondence has been extensively studied for decades. The AdS/CFT correspondence states that a d+1 dimensional quantum gravity in an asymptotic AdS spacetime is equivalent to a d dimensional CFT. In that sense, it is a codimension one holography.

In this talk, we are going to focus on a wedge region in d+1 dimensional AdS. Here, a wedge region is an AdS region which is surrounded by two branes meeting with each other at a corner. We propose a codimension two holography, which claims that the gravity in a specific d+1 dimensional wedge AdS is equivalent to a d-1 dimensional CFT defined on the corner of the wedge. After giving a derivation of the codimension two wedge holography by taking a limit of AdS/BCFT(boundary CFT) setup, we will give an explanation from another perspective, using the brane world holography point of view.

If time is allowed, we will also talk about a construction we proposed for Lorentzian CFT with spacelike boundary and its holographic dual. On the CFT side, this can be realized by considering a Euclidean CFT with an "imaginary" boundary and performing Wick rotation. On the AdS side, this can be realized by taking the tension of the end-of-world brane to "unusual" values. 

[1] I. Akal, Y. Kusuki, T. Takayanagi, Z. Wei,
   "Codimension two holography for wedges,"
   [arXiv:2007.06800 [hep-th]]