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

The p-adic AdS/CFT is a holographic duality based on the p-adic number field ℚp. For a p-adic CFT living on ℚp and with complex-valued fields, the bulk theory is defined on the Bruhat-Tits tree, which can be viewed as the bulk dual of ℚp. We propose that bulk theory can be formulated as a lattice gauge theory of PGL(2, ℚp) 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.