Holography and local fields

TL;DR

This paper reviews recent developments in $p$-adic field theories and their connections to the AdS/CFT correspondence, highlighting potential and challenges in this emerging research area.

Contribution

It provides a summary of recent work on $p$-adic analogues of field theories and discusses their relevance to holography and the AdS/CFT framework.

Findings

Exploration of $p$-adic field theories and their holographic interpretations

Discussion of the utility of $p$-adic models in theoretical physics

Identification of challenges and future directions in $p$-adic holography

Abstract

This paper, which is a summary (in which considerable creative license has been taken) of the author's talk at the sixth international conference on $p$-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017), reviews some recent work connecting field theories defined on the $p$-adic numbers and ideas from the AdS/CFT correspondence. Some results are included, along with general discussion of the utility and interest of $p$-adic analogues of Lagrangian field theories, at least from the author's perspective. A few challenges, shortcomings, and ideas for future work are also discussed.