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Communications in Mathematical Physics

, Volume 352, Issue 3, pp 1019–1059 | Cite as

p-Adic AdS/CFT

  • Steven S. GubserEmail author
  • Johannes Knaute
  • Sarthak Parikh
  • Andreas Samberg
  • Przemek Witaszczyk
Article

Abstract

We construct a p-adic analog to AdS/CFT, where an unramified extension of the p-adic numbers replaces Euclidean space as the boundary and a version of the Bruhat–Tits tree replaces the bulk. Correlation functions are computed in the simple case of a single massive scalar in the bulk, with results that are strikingly similar to ordinary holographic correlation functions when expressed in terms of local zeta functions. We give some brief discussion of the geometry of p-adic chordal distance and of Wilson loops. Our presentation includes an introduction to p-adic numbers.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Steven S. Gubser
    • 1
    Email author
  • Johannes Knaute
    • 2
  • Sarthak Parikh
    • 1
  • Andreas Samberg
    • 3
    • 4
  • Przemek Witaszczyk
    • 5
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrincetonUSA
  2. 2.Institut für Theoretische PhysikTU DresdenDresdenGermany
  3. 3.Institut für Theoretische PhysikRuprecht-Karls-Universität HeidelbergHeidelbergGermany
  4. 4.ExtreMe Matter Institute EMMIGSI Helmholtzzentrum für SchwerionenforschungDarmstadtGermany
  5. 5.Institute of PhysicsJagiellonian UniversityKrakowPoland

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