p-adic CFT is a holographic tensor network

Ling-Yan Hung; Wei Li; Charles M. Melby-Thompson

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arXiv · 1902.01411

p-adic CFT is a holographic tensor network

Ling-Yan Hung·Wei Li·Charles M. Melby-Thompson

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Abstract

The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for a tensor network realization of p-adic AdS/CFT, we prove that the path integral of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in the sense that the tensor network reproduces all correlation functions of the p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as axiomatized by Melzer), and can be applied not only to the p-adic plane, but also to compute any correlation functions on higher genus p-adic curves. Finally, we apply them to define and study RG flows in p-adic CFTs, establishing in particular that any IR fixed point is itself a p-adic CFT.

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Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson. 2019-05-22. p-adic CFT is a holographic tensor network. https://arxiv.org/abs/1902.01411

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