Wilson line networks in $p$-adic AdS/CFT

Abstract

The $p$-adic AdS/CFT is a holographic duality based on the $p$-adic number field ${\mathbb{Q}}_p$. For a $p$-adic CFT living on ${\mathbb{Q}}_p$ and with complex-valued fields, the bulk theory is defined on the Bruhat-Tits tree, which can be viewed as the bulk dual of ${\mathbb{Q}}_p$. We propose that bulk theory can be formulated as a lattice gauge theory of PGL$(2,{\mathbb{Q}}_p)$ on the Bruhat-Tits tree, and show that the Wilson line networks in this lattice gauge theory can reproduce all the correlation functions of the boundary $p$-adic CFT.

34 pages, 5 figures; v2: typos corrected, published version