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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]
+ Show Author Affiliations
  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.
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Dyer, Ethan, Freedman, Daniel Z., & Sully, James. Spinning geodesic Witten diagrams. United States. https://doi.org/10.1007/JHEP11(2017)060
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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.
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@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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https://doi.org/10.1007/JHEP11(2017)060
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text, January 2010

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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

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    Works referencing / citing this record:

    Weight shifting operators and conformal blocks
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    • Nishida, Mitsuhiro; Tamaoka, Kotaro
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    Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
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    • Jepsen, Christian Baadsgaard; Parikh, Sarthak
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    Weight Shifting Operators and Conformal Blocks
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    Fermions in Geodesic Witten Diagrams
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    AdS Weight Shifting Operators
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    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

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