p-Adic AdS/CFT

Steven S. Gubser; Johannes Knaute; Sarthak Parikh; Andreas Samberg; Przemek Witaszczyk

doi:10.1007/s00220-016-2813-6

p-Adic AdS/CFT

Steven S. Gubser, Johannes Knaute, Sarthak Parikh, Andreas Samberg, Przemek Witaszczyk

Physics

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1019-1059
Number of pages	41
Journal	Communications In Mathematical Physics
Volume	352
Issue number	3
DOIs	https://doi.org/10.1007/s00220-016-2813-6
State	Published - Jun 1 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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AU - Knaute, Johannes

AU - Parikh, Sarthak

AU - Samberg, Andreas

AU - Witaszczyk, Przemek

PY - 2017/6/1

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AB - 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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p-Adic AdS/CFT

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