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Title: Growing extra dimensions in AdS/CFT

Abstract

What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFTd data, where “large” means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes D in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop double-discontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large N CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large N, heavy-heavy-light three-point functions, with heavy operators that are parametrically lighter than a power of N, are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of [1], that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy:more » D = d + 1.« less

Authors:
 [1];  [2]
  1. Univ. of Oxford (United Kingdom)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC); Simons Foundation
OSTI Identifier:
1599218
Grant/Contract Number:  
SC0011632; 787185; 488657
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: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal and W Symmetry; Gauge-gravity correspondence

Citation Formats

Alday, Luis F., and Perlmutter, Eric. Growing extra dimensions in AdS/CFT. United States: N. p., 2019. Web. doi:10.1007/JHEP08(2019)084.
Alday, Luis F., & Perlmutter, Eric. Growing extra dimensions in AdS/CFT. United States. https://doi.org/10.1007/JHEP08(2019)084
Alday, Luis F., and Perlmutter, Eric. Mon . "Growing extra dimensions in AdS/CFT". United States. https://doi.org/10.1007/JHEP08(2019)084. https://www.osti.gov/servlets/purl/1599218.
@article{osti_1599218,
title = {Growing extra dimensions in AdS/CFT},
author = {Alday, Luis F. and Perlmutter, Eric},
abstractNote = {What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFTd data, where “large” means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes D in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop double-discontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large N CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large N, heavy-heavy-light three-point functions, with heavy operators that are parametrically lighter than a power of N, are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of [1], that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: D = d + 1.},
doi = {10.1007/JHEP08(2019)084},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2019,
place = {United States},
year = {2019},
month = {8}
}

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Cited by: 13 works
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Double-Trace Deformations of Conformal Correlations
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M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
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Anomalous Dimensions from Crossing Kernels
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The Swampland: Introduction and Review
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