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Title: Spinning geodesic Witten diagrams

Abstract

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al [arXiv:1508.00501] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk three-point interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as a geodesic Witten diagram and the shadow operator formalism.

Authors:
 [1];  [2];  [3]
  1. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Mathematics
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Theory Group; McGill Univ., Montreal, QC (Canada). Dept of Physics
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1410512
Alternate Identifier(s):
OSTI ID: 1418210
Grant/Contract Number:  
AC02-76SF00515; PHY-1316699; PHY-1620045
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; Conformal Field Theory

Citation Formats

Dyer, Ethan, Freedman, Daniel Z., and Sully, James. Spinning geodesic Witten diagrams. United States: N. p., 2017. Web. doi:10.1007/JHEP11(2017)060.
Dyer, Ethan, Freedman, Daniel Z., & Sully, James. Spinning geodesic Witten diagrams. United States. https://doi.org/10.1007/JHEP11(2017)060
Dyer, Ethan, Freedman, Daniel Z., and Sully, James. Fri . "Spinning geodesic Witten diagrams". United States. https://doi.org/10.1007/JHEP11(2017)060. https://www.osti.gov/servlets/purl/1410512.
@article{osti_1410512,
title = {Spinning geodesic Witten diagrams},
author = {Dyer, Ethan and Freedman, Daniel Z. and Sully, James},
abstractNote = {We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al [arXiv:1508.00501] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk three-point interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as a geodesic Witten diagram and the shadow operator formalism.},
doi = {10.1007/JHEP11(2017)060},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}

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Cited by: 7 works
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Works referenced in this record:

Carving out the space of 4D CFTs
journal, May 2012

  • Poland, David; Simmons-Duffin, David; Vichi, Alessandro
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)110

Nonequivalence between conformal covariant Wilson expansion in Euclidean and Minkowski space
journal, September 1972

  • Ferrara, S.; Grillo, A. F.; Parisi, G.
  • Lettere al Nuovo Cimento, Vol. 5, Issue 2
  • DOI: 10.1007/BF02815915

A calculus for higher spin interactions
journal, July 2013

  • Joung, Euihun; Taronna, Massimo; Waldron, Andrew
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)186

Formulas for the eigenvalues of the Laplacian on tensor harmonics on symmetric coset spaces
journal, December 1984

  • Pilch, K.; Schellekens, A. N.
  • Journal of Mathematical Physics, Vol. 25, Issue 12
  • DOI: 10.1063/1.526101

Central charge bounds in 4D conformal field theory
journal, February 2011


Spinning conformal blocks
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)154

Wave Equations in Conformal Space
journal, April 1936

  • Dirac, P. A. M.
  • The Annals of Mathematics, Vol. 37, Issue 2
  • DOI: 10.2307/1968455

The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products
journal, May 1972

  • Ferrara, S.; Grillo, A. F.; Parisi, G.
  • Lettere al Nuovo Cimento, Vol. 4, Issue 4
  • DOI: 10.1007/BF02907130

Spinning conformal correlators
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)071

The group approach to AdS space propagators
journal, September 2003


Conditions on holographic entangling surfaces in higher curvature gravity
journal, June 2014

  • Erdmenger, Johanna; Flory, Mario; Sleight, Charlotte
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)104

Conformal covariant correlation functions
journal, June 1972


Recursion relations for conformal blocks
journal, September 2016

  • Penedones, João; Trevisani, Emilio; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)070

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

Seed conformal blocks in 4D CFT
journal, February 2016

  • Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)183

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


Cubic interaction vertices for massive and massless higher spin fields
journal, December 2006


Higher-spin interactions: four-point functions and beyond
journal, April 2012


Manifestly conformal covariant operator-product expansion
journal, December 1971

  • Ferrara, S.; Grillo, A. F.; Gatto, R.
  • Lettere Al Nuovo Cimento Series 2, Vol. 2, Issue 26
  • DOI: 10.1007/BF02770435

Wave Equations in Conformal Space: Wave Equation for Nucleon
journal, January 1955

  • Murai, Yasuhisa
  • Progress of Theoretical Physics, Vol. 13, Issue 1
  • DOI: 10.1143/ptp.13.109

Higher-spin correlators
journal, October 2013


Properties of partial-wave amplitudes in conformal invariant field theories
journal, April 1975

  • Ferrara, S.; Gatto, R.; Grillo, A. F.
  • Il Nuovo Cimento A, Vol. 26, Issue 3
  • DOI: 10.1007/BF02769009

Radial expansion for spinning conformal blocks
journal, July 2016

  • Costa, Miguel S.; Hansen, Tobias; Penedones, João
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)057

Conformal partial waves and the operator product expansion
journal, February 2004


Rigorous limits on the interaction strength in quantum field theory
journal, April 2010


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


Evaluating the AdS dual of the critical O ( N ) vector model
journal, March 2003


Higher-spin algebras, holography and flat space
journal, February 2017


Finite-component field representations of the conformal group
journal, June 1969


Generating functions of (partially-)massless higher-spin cubic interactions
journal, January 2013

  • Joung, Euihun; Lopez, Luca; Taronna, Massimo
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)168

Bootstrapping 3D fermions
journal, March 2016

  • Iliesiu, Luca; Kos, Filip; Poland, David
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)120

Scalar-vector bootstrap
journal, January 2016

  • Rejon-Barrera, Fernando; Robbins, Daniel
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)139

Deconstructing conformal blocks in 4D CFT
journal, August 2015

  • Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)101

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

Projectors and seed conformal blocks for traceless mixed-symmetry tensors
journal, July 2016

  • Costa, Miguel S.; Hansen, Tobias; Penedones, João
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)018

Improved bounds for CFT’s with global symmetries
journal, January 2012


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

Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011


Worldline approach to semi-classical conformal blocks
journal, July 2015

  • Hijano, Eliot; Kraus, Per; Snively, River
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)131

Bounds on 4D conformal and superconformal field theories
journal, May 2011

  • Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)017

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

Covariant expansion of the conformal four -point function
journal, December 1972


Conformal correlators of mixed-symmetry tensors
journal, February 2015


On the cubic interactions of massive and partially-massless higher spins in (A)dS
journal, July 2012

  • Joung, Euihun; Lopez, Luca; Taronna, Massimo
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)041

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008


Bounds in 4D conformal field theories with global symmetry
journal, December 2010

  • Rattazzi, Riccardo; Rychkov, Slava; Vichi, Alessandro
  • Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 3
  • DOI: 10.1088/1751-8113/44/3/035402

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

Harmony of Spinning Conformal Blocks
text, January 2016

  • Schomerus, Volker; Sobko, Evgeny; Isachenkov, Mikhail
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2017-00888

Higher-spin interactions: four-point functions and beyond
journal, April 2012


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

Spinning AdS propagators
journal, September 2014

  • Costa, Miguel S.; Gonçalves, Vasco; Penedones, João
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)064

Harmony of spinning conformal blocks
journal, March 2017

  • Schomerus, Volker; Sobko, Evgeny; Isachenkov, Mikhail
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)085

Projectors, shadows, and conformal blocks
journal, April 2014


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

Solving the 3D Ising model with the conformal bootstrap
journal, July 2012


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


Towards Feynman rules for Mellin amplitudes in AdS/CFT
journal, October 2011


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

Bounds on 4D Conformal and Superconformal Field Theories
text, January 2010


Central Charge Bounds in 4D Conformal Field Theory
text, January 2010


Bounds in 4D Conformal Field Theories with Global Symmetry
text, January 2010


Spinning Conformal Blocks
text, January 2011


Solving the 3D Ising Model with the Conformal Bootstrap
text, January 2012


On the cubic interactions of massive and partially-massless higher spins in (A)dS
text, January 2012


Projectors, Shadows, and Conformal Blocks
text, January 2012


Generating functions of (partially-)massless higher-spin cubic interactions
text, January 2012


Conditions on holographic entangling surfaces in higher curvature gravity
text, January 2014


Conformal correlators of mixed-symmetry tensors
text, January 2014


Worldline approach to semi-classical conformal blocks
preprint, January 2015


Deconstructing Conformal Blocks in 4D CFT
preprint, January 2015


Bootstrapping 3D Fermions
text, January 2015


Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
text, January 2015


Scalar-Vector Bootstrap
text, January 2015


Seed Conformal Blocks in 4D CFT
text, January 2016


Radial expansion for spinning conformal blocks
text, January 2016


A Stereoscopic Look into the Bulk
text, January 2016


Harmony of Spinning Conformal Blocks
text, January 2016


Anatomy of Geodesic Witten Diagrams
text, January 2017


The group approach to AdS space propagators
text, January 2003


Correlation functions in the CFT(d)/AdS(d+1) correpondence
text, January 1998


Works referencing / citing this record:

Weight shifting operators and conformal blocks
journal, February 2018

  • Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/jhep02(2018)081

Fermions in geodesic Witten diagrams
journal, July 2018

  • Nishida, Mitsuhiro; Tamaoka, Kotaro
  • Journal of High Energy Physics, Vol. 2018, Issue 7
  • DOI: 10.1007/jhep07(2018)149

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
journal, October 2019

  • Jepsen, Christian Baadsgaard; Parikh, Sarthak
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/jhep10(2019)268

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019


Holographic dual of the five-point conformal block
journal, May 2019


Universal lowest-twist in CFTs from holography
journal, August 2019

  • Fitzpatrick, A. Liam; Huang, Kuo-Wei
  • Journal of High Energy Physics, Vol. 2019, Issue 8
  • DOI: 10.1007/jhep08(2019)138

Double-trace deformations of conformal correlations
journal, February 2018

  • Giombi, Simone; Kirilin, Vladimir; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/jhep02(2018)175

AdS weight shifting operators
journal, September 2018


Weight Shifting Operators and Conformal Blocks
text, January 2017


Double-Trace Deformations of Conformal Correlations
text, January 2018


Fermions in Geodesic Witten Diagrams
text, January 2018


AdS Weight Shifting Operators
text, January 2018


The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018


Holographic dual of the five-point conformal block
text, January 2019


Universal Lowest-Twist in CFTs from Holography
text, January 2019