Abstract
Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric. Part of the CFT Distance Conjecture posits that points in this manifold where part of the spectrum becomes free, called higher-spin points, can only be at infinite distance from the interior. There, an infinite tower of operators become conserved currents, and the conformal symmetry is enhanced to a higher-spin algebra. This proposal was initially motivated by the Swampland Distance Conjecture, one of pillars of the Swampland Program. In this work, we show that the conjecture can be tackled using only methods from the conformal toolkit, and without relying on the existence of a weakly-coupled gravity dual. Via conformal perturbation theory combined with properties of correlators and of the higher-spin algebra, we establish that higher-spin points are indeed at infinite distance in the conformal manifold. We make no assumptions besides the usual properties of local CFTs, such as unitarity and the existence of an energy-momentum tensor. In particular, we do not rely on a specific dimension of spacetime (although we assume d > 2), nor do we require the presence of supersymmetry.
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Acknowledgments
We thank A. Antunes, S. Komatsu, M. Montero, K. Papadodimas, F. Tellander, A. Uranga, I. Valenzuela, T. Weigand and A. Zhiboedov for helpful discussions and comments on early versions of the manuscript, as well as E. Skvortsov for helpful correspondence. J.C. would like to thank the Department of Physics at Harvard University and the Instituto de Física Teórica in Madrid for hospitality during early stages of this work. F.B. is supported by the German Research Foundation through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”, by the Swiss National Science Foundation (SNSF), grant number P400P2_194341, and in part by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 Quantum Universe 390833306. The work by J.C. is partially supported by the Spanish Agencia Estatal de Investigacion through the grant “IFT Centro de Excelencia Severo Ochoa CEX2020-001007-S, the grants PGC2018-095976-B-C21 and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/ 501100011033, by ERDF A way of making Europe, and the FPU grant no. FPU17/04181 from the Spanish Ministry of Education.
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Baume, F., Calderón-Infante, J. On higher-spin points and infinite distances in conformal manifolds. J. High Energ. Phys. 2023, 163 (2023). https://doi.org/10.1007/JHEP12(2023)163
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DOI: https://doi.org/10.1007/JHEP12(2023)163