Large spin systematics in CFT

TL;DR

The authors derive a robust, bootstrap-based framework to constrain the large-spin expansion of higher-spin operators in CFTs using analyticity, unitarity, crossing, and conformal partial waves. They prove that perturbative anomalous dimensions and related OPE data organize into expansions with only even powers of the conformal Casimir $J$, establishing the reciprocity principle to all orders and unveiling an infinite set of constraints on structure constants. The non-perturbative analysis yields analogous large-$J$ relations for double-trace–type data, with gamma and OPE coefficients governed by $J^{-\tau_{\min}}$ scalings and parity constraints; gravity-dual and critical $O(N)$ models provide concrete checks. The results extend to non-conformal theories (via dimensional regularization) and offer a powerful, model-independent set of predictions for CFT data, with potential applications to a wide range of theories and bootstrap analyses.

Abstract

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.