2018/04/30 by Petr Kravchuk, David Simmons-Duffin · 1 voice · 20 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep11(2018)102
74 pages plus appendices; v2: fixed typos, updated references, expanded discussion of even spin/odd spin trajectories; v3: fixed some factors of 2
arxiv published 2018/04/30 · openalex created_date 2018/05/07 · openalex publication_date 2018/11/01 · arxiv created 2019/08/26 · arxiv updated 2019/08/27 · openalex updated_date 2026/07/31
We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J, light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal block. This gives a simple derivation of Caron-Huot's Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the average null energy condition (ANEC), and furthermore generalize the ANEC to continuous spin.