Higher Spin ANEC and the Space of CFTs

Abstract

We study the positivity properties of the leading Regge trajectory in higher-dimensional, unitary, conformal field theories (CFTs). These conditions correspond to higher spin generalizations of the averaged null energy condition (ANEC). By studying higher spin ANEC, we will derive new bounds on the dimensions of charged, spinning operators and prove that if the Hofman-Maldacena bounds are saturated, then the theory has a higher spin symmetry. We also derive new, general bounds on CFTs, with an emphasis on theories whose spectrum is close to that of a generalized free field theory. As an example, we consider the Ising CFT and show how the OPE structure of the leading Regge trajectory is constrained by causality. Finally, we use the analytic bootstrap to perform additional checks, in a large class of CFTs, that higher spin ANEC is obeyed at large and finite spin. In the process, we calculate corrections to large spin OPE coefficients to one-loop and higher in holographic CFTs.

arXiv comment48 pages, 5 figures, v2: references added

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• Carving out OPE space and precise $O(2)$ model critical exponents
• Unitarity Methods in AdS/CFT
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Black Holes and Conformal Regge Bootstrap
• Recursion relations for 5-point conformal blocks
• Opacity from Loops in AdS
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• On Local and Integrated Stress-Tensor Commutators
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Detector Operators for Celestial Symmetries
• Implications of ANEC for SCFTs in four dimensions
• The Inversion Formula and 6j Symbol for 3d Fermions
• A CFT Distance Conjecture
• Freedom near Lightcone and ANEC Saturation
• On the Stress Tensor Light-ray Operator Algebra
• Higher-spin localized shocks