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A CFT distance conjecture

Perlmutter, Eric and Rastelli, Leonardo and Vafa, Cumrun and Valenzuela, Irene (2021) A CFT distance conjecture. Journal of High Energy Physics, 2021 (10). Art. No. 70. ISSN 1029-8479. doi:10.1007/jhep10(2021)070.

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We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

Item Type:Article
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URLURL TypeDescription Paper
Valenzuela, Irene0000-0002-6658-8121
Additional Information:© 2021 The Authors. 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. Article funded by SCOAP3. Received: May 5, 2021; Accepted: September 10, 2021; Published: October 8, 2021. We wish to thank Chris Beem, Jan de Boer, Sergio Cecotti, Tristan Collins, Daniel Jafferis, Zohar Komargodski, Jacob McNamara, Carlo Meneghelli, Miguel Montero, Kyriakos Papadodimas, Shlomo Razamat, Yuji Tachikawa, Arnav Tripathy and Shing-Tung Yau for helpful discussions. E.P. is supported in part by the World Premier International Research Center Initiative, MEXT, Japan, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The research of L.R. is supported in part by NSF grant No. PHY-1915093. The research of C.V. and I.V. was supported in part by a grant from the Simons Foundation (602883, CV). The research of C.V. was also supported by the National Science Foundation under Grant No. NSF PHY-2013858. We thank the KITP for hospitality during the course of this work, which was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons Foundation602883
Subject Keywords:AdS-CFT Correspondence; Conformal Field Theory
Issue or Number:10
Record Number:CaltechAUTHORS:20211022-171956757
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Official Citation:Perlmutter, E., Rastelli, L., Vafa, C. et al. A CFT distance conjecture. J. High Energ. Phys. 2021, 70 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111606
Deposited By: Tony Diaz
Deposited On:22 Oct 2021 23:49
Last Modified:26 Oct 2021 16:32

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