Crossing symmetry and Higher spin towers

TL;DR

This paper explores how crossing symmetry constrains the spectrum and structure constants of higher spin operators in weakly coupled gauge conformal field theories, revealing universal behaviors and connections to supergravity and Wilson loops.

Contribution

It derives all-loop constraints on higher spin spectra and structure constants using crossing symmetry, and connects these results to supergravity computations and Wilson loop correlators.

Findings

Universal large spin structure constants with pole structures matching supergravity predictions

All-loop expressions for the double null limit of mixed correlators

Crossing symmetry relates different higher spin towers and constrains their spectra

Abstract

We consider higher spin operators in weakly coupled gauge conformal field theories. Crossing symmetry of mixed scalar correlators relates different higher spin towers and we study the consequences for the spectrum and structure constants of higher spin operators of different twists. Constraints are obtained to all loops in perturbation theory. The large spin contributions to the structure constants can be resummed into a theory-dependent prefactor times a universal factor, whose structure of poles agrees with the one that would be obtained from a Witten diagram supergravity computation, although only crossing symmetry is assumed. Finally, our results provide an all loop expression for the double null limit of mixed correlators, which is in perfect agreement with the correlator/Wilson loop correspondence.