Title: Geodesic bulk diagrams on the Bruhat–Tits tree

Abstract

Geodesic bulk diagrams were recently shown to be the geometric objects which compute global conformal blocks. We show that this duality continues to hold in p-adic AdS/CFT, where the bulk is replaced by the Bruhat-Tits tree, an infinite regular graph with no cycles, and the boundary is described by p-adic numbers, rather than reals. We apply the duality to evaluate the four-point function of scalar operators of generic dimensions using tree-level bulk diagrams. Relative to standard results from the literature, we find intriguing similarities as well as significant simplifications. Notably, all derivatives disappear in the conformal block decomposition of the four-point function. On the other hand, numerical coefficients in the four-point function as well as the structure constants take surprisingly universal forms, applicable to both the reals and the p-adics when expressed in terms of local zeta functions. Finally, we present a minimal bulk action with nearest neighbor interactions on the Bruhat-Tits tree, which reproduces the two-, three-, and four-point functions of a free boundary theory.

Authors:

Gubser, Steven S. ^[1]; Parikh, Sarthak ^[1]

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+ Show Author Affiliations

1. Princeton Univ., NJ (United States)

Publication Date:

Thu Sep 21 00:00:00 EDT 2017

Research Org.:

Princeton Univ., NJ (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

OSTI Identifier:

1600653

Alternate Identifier(s):

OSTI ID: 1393709

Grant/Contract Number:  

SC0007968; FG02-91ER40671; PHY-1066293

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review D

Additional Journal Information:

Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal field theory; guage-gravity dualities