# Tensor network and ($p$-adic) AdS/CFT

## TL;DR

This paper constructs a tensor network on the Bruhat-Tits tree to concretely realize the $p$-adic AdS/CFT correspondence, demonstrating how key holographic features emerge naturally from the network.

## Contribution

It provides a concrete tensor network model for $p$-adic AdS/CFT, illustrating bulk reconstruction and boundary correlator computation without assuming the duality.

## Key findings

- Tensor network on Bruhat-Tits tree models $p$-adic AdS/CFT
- Bulk operator reconstruction is naturally realized
- Boundary correlators are computed holographically

## Abstract

We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed $p$-adic AdS/CFT correspondence (a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$). Instead of assuming the $p$-adic AdS/CFT correspondence, we show how important features of AdS/CFT such as the bulk operator reconstruction and the holographic computation of boundary correlators are automatically implemented in this tensor network.