Growing extra dimensions in AdS/CFT

  • Luis F. Alday
  • Eric PerlmutterEmail author
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Conformal and W Symmetry Gauge-gravity correspondence 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordU.K.
  2. 2.Walter Burke Institute for Theoretical PhysicsCaltechPasadenaU.S.A.

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