Growing extra dimensions in AdS/CFT

Author: 

Alday, L
Perlmutter, E

Publication Date: 

19 August 2019

Journal: 

JOURNAL OF HIGH ENERGY PHYSICS

Last Updated: 

2020-02-03T12:56:09.103+00:00

Issue: 

8

Volume: 

2019

DOI: 

10.1007/JHEP08(2019)084

abstract: 

© 2019, The Author(s). 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.

Symplectic id: 

1054166

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article