p-adic CFT is a holographic tensor network

Abstract

A bstract 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 [1] 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.