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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.
Publication Date: Jun-2017
Electronic Publication Date: 16-Jan-2017
Citation: Gubser, Steven S, Knaute, Johannes, Parikh, Sarthak, Samberg, Andreas, Witaszczyk, Przemek. (2017). p-Adic AdS/CFT. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 353 (1019 - 1059. doi:10.1007/s00220-016-2813-6
DOI: doi:10.1007/s00220-016-2813-6
ISSN: 0010-3616
EISSN: 1432-0916
Pages: 1019 - 1059
Type of Material: Journal Article
Version: Author's manuscript

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