Anomalous dimensions of high-spin operators beyond the leading order

TL;DR

This paper uncovers a universal parity-preserving structure in the large-N expansion of twist-two anomalous dimensions across QCD and supersymmetric theories. By introducing a scaling function f(N) that encodes conformal-spin-based corrections and incorporating beta-function effects, it derives an infinite set of MVV-like relations linking subleading 1/N corrections to lower-order terms. The authors demonstrate these relations at two and three loops, in the large β0 limit, and in strong coupling via AdS/CFT for higher-twist scalars in N=4 SYM. The results illuminate a deep connection between conformal symmetry, reciprocity, and the organization of perturbative corrections, with potential implications for higher twists and integrability-based approaches.

Abstract

Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading corrections suppressed by powers of the Lorentz spin. We argue that this structure is a manifestation of the `self-tuning' property of the multi-loop anomalous dimensions - in a conformal gauge theory, the anomalous dimension of Wilson operators is a function of their conformal spin which is modified in higher loops by an amount proportional to the anomalous dimension. Making use of the parity property of this function and incorporating the beta-function contribution, we demonstrate the existence of (infinite number of) relations between subleading corrections to the twist-two anomalous dimensions in QCD and its supersymmetric extensions. They imply that the subleading corrections to the anomalous dimensions suppressed by odd powers of the conformal spin can be expressed in terms of the lower-loops corrections suppressed by smaller even powers of the spin. We show that these relations hold true in QCD to all loops in the large beta0 limit. In the N=4 SYM theory, we employ the AdS/CFT correspondence to argue that the same relations survive in the strong coupling regime for higher-twist scalar operators dual to a folded string rotating on the AdS3xS1.