Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory

TL;DR

This paper proposes an all-loop asymptotic Baxter equation for calculating anomalous dimensions in N=4 super-Yang-Mills theory, based on perturbative data, and derives an integral equation for the cusp anomalous dimension.

Contribution

It introduces a novel all-loop Baxter equation for spectrum determination in N=4 SYM, extending perturbative results and providing a new integral equation for the cusp anomalous dimension.

Findings

Proposed an all-loop Baxter equation for anomalous dimensions.

Derived an integral equation for the cusp anomalous dimension.

Validated the asymptotic expansion for large conformal spin.

Abstract

Relying on a few lowest order perturbative calculations of anomalous dimensions of gauge invariant operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in maximally supersymmetric gauge theory, we propose an all-loop generalization of the Baxter equation which determines their spectrum. The equation does not take into account wrapping effects and is thus asymptotic in character. We develop an asymptotic expansion of the deformed Baxter equation for large values of the conformal spin and derive an integral equation for the cusp anomalous dimension.