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arXiv · 1812.07331

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

Aritra Banerjee·Abhishek Chowdhury·Somyadip Thakur·Gang Yang
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Abstract

We study non-perturbative interpolating functions to probe the physics of anomalous dimensions associated with twist-two operators in ${\cal N}=4$ 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 Pad\'{e} approximants and its generalizations . For the finite $N$ case, ${\cal N}=4$ 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.

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Aritra Banerjee, Abhishek Chowdhury, Somyadip Thakur, Gang Yang. 2018-12-18. On interpolating anomalous dimension of twist-two operators with general spins. https://doi.org/10.1007/jhep07(2019)086

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