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Shocks, Superconvergence, and a Stringy Equivalence Principle

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arxiv 1904.05905 v1 pith:WNKDIUYU submitted 2019-04-11 hep-th

Murat Kologlu , Petr Kravchuk , David Simmons-Duffin , Alexander Zhiboedov This is my paper · ORCID
classification hep-th
keywords operatorscommutativitygravitationalshockshockssuperconvergenceaneccommute
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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