Analytic solution of the multiloop Baxter equation

TL;DR

This paper develops an analytical method using Wilson polynomials and Mellin transforms to solve the multiloop Baxter equation, enabling precise calculation of anomalous dimensions in supersymmetric gauge theories.

Contribution

It introduces a novel formalism for solving the multiloop Baxter equation analytically, bypassing maximal transcendentality, and confirms known four-loop results while determining five-loop dressing contributions.

Findings

Analytical solutions for multiloop anomalous dimensions

Confirmation of four-loop results

Determination of five-loop dressing parts

Abstract

The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its $sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.