p-Adic AdS/CFT

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2017-06, Vol.352 (3), p.1019-1059
Main Authors: Gubser, Steven S., Knaute, Johannes, Parikh, Sarthak, Samberg, Andreas, Witaszczyk, Przemek
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Euclidean geometry
Euclidean space
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2813-6