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.