Fine structure of anomalous dimensions in N=4 super Yang-Mills theory

TL;DR

This paper investigates the detailed structure of anomalous dimensions in high-twist Wilson operators within planar N=4 super Yang-Mills theory, using integrability techniques to analyze their spectrum and corrections.

Contribution

It provides a systematic analysis of the fine structure of anomalous dimensions in the SL(2) sector using Baxter equations and semiclassical methods, revealing their asymptotic behavior and perturbative modifications.

Findings

Derived leading asymptotic expressions for trajectories

Analyzed ground and excited state properties

Identified perturbative corrections to the spectrum

Abstract

Anomalous dimensions of high-twist Wilson operators in generic gauge theories occupy a band of width growing logarithmically with their conformal spin. We perform a systematic study of its fine structure in the autonomous SL(2) subsector of the dilatation operator of planar N=4 super Yang-Mills theory which is believed to be integrable to all orders in 't Hooft coupling. We resort in our study on the framework of the Baxter equation to unravel the properties of the ground state trajectory and the excited trajectories in the spectrum. We use two complimentary approaches in our analysis based on the asymptotic solution of the Baxter equation and on the semiclassical expansion to work out the leading asymptotic expression for the trajectories in the upper and lower part of the band and to find how they are modified by the perturbative corrections.