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 padic AdS/CFT, where the bulk is replaced by the BruhatTits tree, an infinite regular graph with no cycles, and the boundary is described by padic numbers, rather than reals. We apply the duality to evaluate the fourpoint function of scalar operators of generic dimensions using treelevel 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 fourpoint function. On the other hand, numerical coefficients in the fourpoint function as well as the structure constants take surprisingly universal forms, applicable to both the reals and the padics when expressed in terms of local zeta functions. Finally, we present a minimal bulk action with nearest neighbor interactions on the BruhatTits tree, which reproduces the two, three, and fourpoint functions of a free boundary theory.
 Authors:

 Princeton Univ., NJ (United States)
 Publication Date:
 Research Org.:
 Princeton Univ., NJ (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); National Science Foundation (NSF)
 OSTI Identifier:
 1600653
 Alternate Identifier(s):
 OSTI ID: 1393709
 Grant/Contract Number:
 SC0007968; FG0291ER40671; PHY1066293
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal field theory; guagegravity dualities
Citation Formats
Gubser, Steven S., and Parikh, Sarthak. Geodesic bulk diagrams on the Bruhat–Tits tree. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.066024.
Gubser, Steven S., & Parikh, Sarthak. Geodesic bulk diagrams on the Bruhat–Tits tree. United States. doi:10.1103/PhysRevD.96.066024.
Gubser, Steven S., and Parikh, Sarthak. Thu .
"Geodesic bulk diagrams on the Bruhat–Tits tree". United States. doi:10.1103/PhysRevD.96.066024. https://www.osti.gov/servlets/purl/1600653.
@article{osti_1600653,
title = {Geodesic bulk diagrams on the Bruhat–Tits tree},
author = {Gubser, Steven S. and Parikh, Sarthak},
abstractNote = {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 padic AdS/CFT, where the bulk is replaced by the BruhatTits tree, an infinite regular graph with no cycles, and the boundary is described by padic numbers, rather than reals. We apply the duality to evaluate the fourpoint function of scalar operators of generic dimensions using treelevel 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 fourpoint function. On the other hand, numerical coefficients in the fourpoint function as well as the structure constants take surprisingly universal forms, applicable to both the reals and the padics when expressed in terms of local zeta functions. Finally, we present a minimal bulk action with nearest neighbor interactions on the BruhatTits tree, which reproduces the two, three, and fourpoint functions of a free boundary theory.},
doi = {10.1103/PhysRevD.96.066024},
journal = {Physical Review D},
number = 6,
volume = 96,
place = {United States},
year = {2017},
month = {9}
}
Web of Science
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