Crossing symmetry and Higher spin towers

TL;DR

The paper investigates how crossing symmetry constrains towers of higher spin operators in weakly coupled gauge CFTs, including mixed scalar correlators that mix different twists. Using an analytic bootstrap approach, it derives all-loop integral relations that fix the large-spin spectrum and OPE data, showing that anomalous dimensions scale as $\gamma_\ell \sim f(g)\log\ell$ and that three-point couplings to external scalars take the universal form $C_{pq\ell} \sim \Gamma\left(\frac{\Delta_p+\Delta_q-\tau_\ell}{2}\right)$, up to degeneracy-averaged corrections. The leading twist analysis yields a universal, gravity-like pole structure in the premultipliers, and the authors obtain an all-loop expression for the double-null limit that agrees with the correlator/Wilson loop correspondence. The results are illustrated in ${\cal N}=4$ SYM, where crossing and $SU(4)_R$ representations organize the higher-spin towers and reproduce known loop data, signaling a deep link between crossing, large-spin dynamics, and holographic expectations. Overall, the work provides a robust, all-loop framework tying spectral data, OPE coefficients, and nonlocal limits together via crossing symmetry.

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.

Figures (2)

• Figure 1: Crossing symmetry
• Figure 2: As consecutive insertion points become null separated in space-time they form a rectangle $(A,B,C,D)$ in the $(\sigma,\tau)$ coordinates.