High Energy Theory Seminar

I will give a first-principles introduction to p-adic numbers and p-adic AdS/CFT. p-adic numbers are an alternative to the real numbers, and they have a hierarchical structure which lends itself naturally to a holographic construction. The bulk dual to a p-adic boundary is the so-called Bruhat-Tits tree, an infinite regular graph. A bulk-boundary correspondence can be set up starting from a classical action in the bulk, and correlation functions exhibit properties surprisingly similar to the ones derived in standard AdS/CFT. The ultrametricity of the p-adic numbers implies some simplifications of both the four-point function and the operator product algebra. I will also review a few results in p-adic field theory, both perturbative and non-perturbative.