Effective field theory on a finite boundary of the Bruhat-Tits tree

TL;DR

This paper derives an effective boundary theory from the Bruhat-Tits tree using $p$-adic AdS/CFT duality, enabling the computation of two-point functions for a deformed $p$-adic conformal field theory.

Contribution

It introduces a method to obtain boundary effective theories on finite Bruhat-Tits trees and computes two-point functions within the $p$-adic AdS/CFT framework.

Findings

Two-point functions are derived from the effective boundary action.

The boundary theory corresponds to a deformed $p$-adic conformal field theory.

The approach links bulk reconstruction to boundary correlators in $p$-adic geometry.

Abstract

Based on bulk reconstruction from the finite boundary of the Bruhat-Tits tree, the boundary effective theory is obtained after integrating out fields outside this boundary. According to the $~p$-adic version of Anti-de Sitter/Conformal Field Theory duality, two-point functions of dual theory living on the finite boundary are read out from the effective action. They can be regarded as two-point functions of a deformed conformal field theory over $~p$-adic numbers.