# A $p$-adic version of AdS/CFT

## TL;DR

This paper explores a novel $p$-adic holographic duality where classical dynamics on an infinite tree graph corresponds to a conformal field theory over $p$-adic numbers, revealing simplified structures and parallels to traditional AdS/CFT.

## Contribution

It introduces a $p$-adic version of AdS/CFT, demonstrating how classical tree dynamics relate to $p$-adic conformal field theories and analyzing their correlators and loop diagrams.

## Key findings

- Holographic three- and four-point functions computed for $p$-adic theories
- Comparison of $p$-adic correlators with ordinary field theories
- Identification of simplified structures in $p$-adic holography

## Abstract

In this summary of my talk at Strings 2016, I explain how classical dynamics on an infinite tree graph can be dual to a conformal field theory defined over the $p$-adic numbers. An informal introduction to $p$-adic numbers is followed by a presentation of results on holographic three- and four-point functions. The simplicity of $p$-adic field theories and their similarity to ordinary field theories are illustrated through comparisons of holographic correlators and computations of simple loop diagrams on the field theory side. I close with a discussion of challenges and directions for future work.