Large spin systematics in CFT

TL;DR

This paper derives an infinite set of constraints on the behavior of large spin operators in conformal field theories, using fundamental principles like analyticity, unitarity, and crossing symmetry, applicable to both perturbative and non-perturbative regimes.

Contribution

It introduces a comprehensive set of constraints on large spin expansions in CFTs, proving reciprocity principles to all orders and extending results beyond conformal theories.

Findings

Proof of reciprocity principle for anomalous dimensions to all orders.

New reciprocity principle for structure constants.

Constraints applicable to both perturbative and non-perturbative CFTs.

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.