In this talk I will explore recently proposed tensor networks/AdS correspondence based on the quantum error correcting model. Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we will find that the physical wave function generically do not admit any connected correlation functions of local operators. As we know computation of correlation functions plays an important role in establishing AdS/CFT duality, so we will like to remedy this problem. In this talk, I will give a proposal for computing connected two and three point functions and we will see there is a possibility of the emergence of the analogues of Witten diagrams in the tensor network. Using the Coxeter construction, I will describe how to construct the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides and show that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region. Also I will briefly mention how to construct the bulk isometry generators in terms of Coxeter tessellations thereby taking a step towards establishing the bulk/boundary symmetry matching and solidifying the AdS/CFT dictionary.

 

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