skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
 [1];  [1]
  1. 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) (SC-25); 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

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 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.},
doi = {10.1103/PhysRevD.96.066024},
journal = {Physical Review D},
number = 6,
volume = 96,
place = {United States},
year = {2017},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Nonarchimedean Conformal Field Theories
journal, November 1989


Scalar models of p-adic quantum field theory and hierarchical models
journal, February 1989

  • Lerner, �. Yu.; Missarov, M. D.
  • Theoretical and Mathematical Physics, Vol. 78, Issue 2
  • DOI: 10.1007/BF01018683

Renormalization group in a fermionic hierarchical model
journal, November 1994

  • Lerner, �. Yu.; Missarov, M. D.
  • Theoretical and Mathematical Physics, Vol. 101, Issue 2
  • DOI: 10.1007/BF01018283

Critical Exponents in p-Adic ϕ4-Model
conference, January 2006

  • Missarov, Moukadas D.
  • p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference, AIP Conference Proceedings
  • DOI: 10.1063/1.2193117

Epsilon-expansion in the N-component ϕ 4 model
journal, March 2006


p-Adic AdS/CFT
journal, January 2017

  • Gubser, Steven S.; Knaute, Johannes; Parikh, Sarthak
  • Communications in Mathematical Physics, Vol. 352, Issue 3
  • DOI: 10.1007/s00220-016-2813-6

Edge length dynamics on graphs with applications to p-adic AdS/CFT
journal, June 2017

  • Gubser, Steven S.; Heydeman, Matthew; Jepsen, Christian
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)157

Loops in AdS from conformal field theory
journal, July 2017

  • Aharony, Ofer; Alday, Luis F.; Bissi, Agnese
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)036

A scaling theory for the long-range to short-range crossover and an infrared duality
journal, August 2017

  • Behan, Connor; Rastelli, Leonardo; Rychkov, Slava
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 35
  • DOI: 10.1088/1751-8121/aa8099

Non-archimedean strings and Bruhat-Tits trees
journal, September 1989

  • Zabrodin, A. V.
  • Communications in Mathematical Physics, Vol. 123, Issue 3
  • DOI: 10.1007/BF01238811

Adelic string amplitudes
journal, December 1987


Adelic string N-point amplitudes
journal, January 1989


Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

  • Hijano, Eliot; Kraus, Per; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)146

Anti de Sitter space and holography
journal, January 1998


Correlation functions in the CFTd/AdSd+1 correspondence
journal, April 1999


Conformal four point functions and the operator product expansion
journal, April 2001


A stereoscopic look into the bulk
journal, July 2016

  • Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)129

Scattering in anti–de Sitter space and operator product expansion
journal, October 1999


Holography in 4D (super) higher spin theories and a test via cubic scalar couplings
journal, July 2005


Higher-Spin Gauge Theories in Four, Three and two Dimensions
journal, December 1996


An AdS 3 dual for minimal model CFTs
journal, March 2011


Minimal model holography
journal, May 2013


Quartic AdS interactions in higher-spin gravity from Conformal Field Theory
journal, November 2015

  • Bekaert, X.; Erdmenger, J.; Ponomarev, D.
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)149

Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings
journal, May 2016


Towards holographic higher-spin interactions: four-point functions and higher-spin exchange
journal, March 2015

  • Bekaert, X.; Erdmenger, J.; Ponomarev, D.
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)170

A Mellin space approach to the conformal bootstrap
journal, May 2017

  • Gopakumar, Rajesh; Kaviraj, Apratim; Sen, Kallol
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)027

Geodesic Witten diagrams with an external spinning field
journal, May 2017

  • Nishida, Mitsuhiro; Tamaoka, Kotaro
  • Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 5
  • DOI: 10.1093/ptep/ptx055

Geodesic diagrams, gravitational interactions & OPE structures
journal, June 2017

  • Castro, Alejandra; Llabrés, Eva; Rejon-Barrera, Fernando
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)099

Anatomy of geodesic Witten diagrams
journal, May 2017

  • Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)070

Spinning Witten diagrams
journal, June 2017

  • Sleight, Charlotte; Taronna, Massimo
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)100

AdS dual of the critical O(N) vector model
journal, December 2002


Consistent equations for interacting gauge fields of all spins in 3+1 dimensions
journal, July 1990


More on equations of motion for interacting massless fields of all spins in 3+1 dimensions
journal, July 1992