Exploring the tensor networks/AdS correspondence

Bhattacharyya, Arpan and Gao, Zhe-Shen and Hung, Ling-Yan and Liu, Si-Nong (2016) Exploring the tensor networks/AdS correspondence. In: JOURNAL OF HIGH ENERGY PHYSICS (8).

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Abstract

In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found 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 A.

Item Type:	Journal Article
Publication:	JOURNAL OF HIGH ENERGY PHYSICS
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	17 Feb 2017 09:11
Last Modified:	17 Feb 2017 09:11
URI:	http://eprints.iisc.ac.in/id/eprint/56262

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