TH String Theory Seminar

p-adic AdS/CFT

by Steven Gubser (Princeton)

4-3-006 - TH Conference Room (CERN)

4-3-006 - TH Conference Room


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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.  A version of gravitational dynamics can be defined on the tree in terms of a graph-theoretic Ricci tensor.  The result is a non-linear theory of massless edge length fluctuations dual to an operator with some features in common with the stress tensor.

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