Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2020)096
Keywords
AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field; Theory; Models of Quantum Gravity
Categories
Funding
- Simons Foundation [488657]
- Sloan Research Fellowship
- DOE Early Career Award [DE-SC0019085]
- DOE [DE-SC0009988]
- National Science Foundation [NSF PHY-1748958]
- U.S. Department of Energy, Office of Science, Office of High Energy Physics [DE-SC0011632]
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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-cc in terms of the OPE data of single-trace operators.
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