On interpolating anomalous dimension of twist-two operators with general spins

Abstract

Abstract We study non-perturbative interpolating functions to probe the physics of anomalous dimensions associated with twist-two operators in $$ \mathcal{N}=4 $$ N = 4 SYM of finite and infinite spin. Compared to previous studies, the novel result of this paper is to introduce single multivariate functions of both coupling g and spin j to approximate such anomalous dimensions. We provide a unified framework to study such operators in interim ranges of the parameters which so far has eluded previous results. Explicitly, we consider twist-two anomalous dimensions in two distinct scenarios using interpolating functions. For the large N case, we stick to simple Padé approximants and its generalizations. For the finite N case, $$ \mathcal{N}=4 $$ N = 4 SYM is expected to be S-dual invariant, hence the observables are expected be modular invariant. To probe the finite N physics, we take into account the non-planar and instanton contributions by constructing modular invariant interpolating functions to approximate the cusp and twist-two anomalous dimensions. We also consider interpolating functions for the twist-four operators and study level crossing phenomenon between the twist-two and twist-four operators.