A p-adic version of AdS/CFT

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.