Aspects of 𝑝-adic geometry related to entanglement entropy

Abstract

The replica argument for the computation of entanglement entropy is based on Rényi entropies computed over cyclic branched coverings of a Riemann surface. The recent development of a p p -adic approach to AdS/CFT holography suggests that this computational method should have an analog in p p -adic geometry. The purpose of this survey paper is to outline some aspects of p p -adic geometry that are naturally related to the problem of formulating an analog of the usual replica argument for entanglement entropy in the context of p p -adic holography.