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.
Highlights
This positivity condition was first studied extensively for conformal field theories (CFTs) in [4] to derive universal bounds on three-point functions involving Tμν
We study the positivity properties of the leading Regge trajectory in higherdimensional, unitary, conformal field theories (CFTs)
We have focused on how HS averaged null energy condition (ANEC) constrains fundamental CFT data, but we will take the reverse approach and study if predictions from the bootstrap are always compatible with HS ANEC
Summary
In CFTs, the higher spin positivity conditions bound OPE coefficients which are computable using large spin expansions. In the context of large N CFTs, this implies AdS theories with only cubic interactions are consistent with HS ANEC at tree and one-loop level, with the corresponding restrictions on spin. We present new results for large spin OPE coefficients to all orders in 1/N for holographic CFTs. In the dual AdS theory, these OPE coefficients can be found through conformal block decompositions of ladder diagrams.
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