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Growing Extra Dimensions in AdS/CFT

Alday, Luis F. and Perlmutter, Eric (2019) Growing Extra Dimensions in AdS/CFT. . (Unpublished)

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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 CFT$_d$ 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 arXiv:0908.0756, that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: D=d+1.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:We thank Ofer Aharony, Chris Beem, David Berenstein, Agnese Bissi, Scott Collier, Frank Coronado, Xi Dong, Sergei Gukov, Ben Heidenreich, Ying Hsuan-Lin, Shamit Kachru, Shota Komatsu, Dalimil Mazáč, David Meltzer, Yi Pang, Leonardo Rastelli and David SimmonsDuffin for helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 787185). We thank CERN during the workshop “Advances in Quantum Field Theory,” and the International Institute of Physics, Natal during the workshop “Nonperturbative Methods for Conformal Theories,” for stimulating environments. EP thanks the University of Michigan and KITP for hospitality during the course of this work. EP is supported by Simons Foundation grant 488657 and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Department of Energy (DOE)DE-SC0011632
European Research Council (ERC)787185
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Record Number:CaltechAUTHORS:20190709-155348710
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97016
Deposited By: Joy Painter
Deposited On:09 Jul 2019 23:39
Last Modified:09 Jul 2019 23:39

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