p-adic CFT is a holographic tensor network

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.

43 pages, 13 figures; v2: typos corrected, published version

References in corpus (10)

• Entanglement renormalization
• Tensor renormalization group approach to 2D classical lattice models
• Holographic representation of local bulk operators
• Tensor Network Renormalization
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Loop optimization for tensor network renormalization
• Renormalization group flows of Hamiltonians using tensor networks
• Tensor network and ($p$-adic) AdS/CFT
• Geodesic bulk diagrams on the Bruhat-Tits tree

Cited by in corpus (2)

• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• The boundary theory of a spinor field theory on the Bruhat-Tits tree