Shocks, superconvergence, and a stringy equivalence principle
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Springer
Received: June 8, 2020 Accepted: October 5, 2020 Published: November 19, 2020
Murat Koloğlu,a Petr Kravchuk,b David Simmons-Duffina and Alexander Zhiboedovc a
Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, U.S.A. b School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A. c CERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering — in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain “superconvergence sum rule.” In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators. In a planar 4d CFT, these sum rules express a−c c in terms of the OPE data of single-trace operators. Keywords: AdS-CFT Correspondence, Conformal and W Symmetry, Conformal Field Theory, Models of Quantum Gravity ArXiv ePrint: 1904.05905
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)096
JHEP11(2020)096
Shocks, superconvergence, and a stringy equivalence principle
Contents 1 Introduction
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3 Event shapes in CFT and shocks in AdS 3.1 Review: the light transform 3.2 Review: event shapes 3.3 Computing event shapes in the bulk
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4 Products of light-ray operators and commutativity 4.1 Existence vs. commutativity 4.2 Convergence of the Wightman function integral 4.2.1 OPE limit on the first sheet 4.2.2 Lightcone limit on the first sheet 4.2.3 Rindler positivity 4.2.4 Regge limit 4.2.5 Lightcone limit on the second sheet 4.2.6 Asymptotic ligthcone expansion 4.3 Convergence of the double commutator integral 4.4 Summary of non-perturbative convergence conditions 4.5 Convergence in perturbation theory 4.6 Other types of null-integrated operators
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JHEP11(2020)096
2 Shocks and superconvergence in flat space 2.1 Shockwave amplitudes 2.2 Shock commutativity and the Regge limit 2.2.1 Spinning shocks 2.3 Shock commutativity in General Relativity 2.3.1 Minimally-coupled scalar 2.3.2 Minimally-coupled photon 2.3.3 Gravitons 2.4 Non-minimal couplings 2.4.1 Non-minimally coupled photons 2.4.2 Higher derivative gravity 2.5 Gr
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