Holography and local fields

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.

arXiv comment26 pages, no figures to speak of. The talk on which this proceeding is based was delivered at the sixth international conference on p-adic mathematical physics and its applications, held at CINVESTAV, Mexico City, October 23--27, 2017