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Title: Growing extra dimensions in AdS/CFT

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Univ. of Oxford (United Kingdom); Caltech
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
+ Show Author Affiliations

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.

Research Organization:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
European Research Council (ERC); Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0011632
OSTI ID:
1599218
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2019; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Holographic three-point functions of semiclassical states text January 2010
Emergent Spacetime and Holographic CFTs text January 2011
Constraints on 2d CFT partition functions text January 2013
Naturalness and the Weak Gravity Conjecture text January 2014
Universal Spectrum of 2d Conformal Field Theory in the Large c Limit text January 2014
Lessons from crossing symmetry at large N preprint January 2014
Evidence for a Lattice Weak Gravity Conjecture text January 2016
Eigenstate Thermalization Hypothesis in Conformal Field Theory text January 2016
Quantum Gravity from Conformal Field Theory text January 2017
Unmixing Supergravity text January 2017
Supersymmetry Breaking by Fluxes text January 2017
How to Succeed at Holographic Correlators Without Really Trying text January 2017
Double-Trace Deformations of Conformal Correlations text January 2018
Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications text January 2018
M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture text January 2018
Anomalous Dimensions from Crossing Kernels text January 2018
All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry text January 2018
The Swampland: Introduction and Review text January 2019
Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry text January 2001
Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills text January 2002
On semiclassical approximation and spinning string vertex operators in AdS_5 x S^5 text January 2003
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Cited By (5)

Bound on asymptotics of magnitude of three point coefficients in 2D CFT journal January 2020
The holographic landscape of symmetric product orbifolds journal January 2020
Quantum log-corrections to swampland conjectures journal February 2020
Bound on asymptotics of magnitude of three point coefficients in 2D CFT text January 2019
Quantum Log-Corrections to Swampland Conjectures text January 2019

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT Correspondence
Conformal and W Symmetry
Gauge-gravity correspondence