Functional BES equation

TL;DR

This paper reformulates the BES equation for planar N=4 supersymmetric gauge theory into a system of functional equations, enabling perturbative solutions at strong coupling and reproducing known recursive results.

Contribution

It introduces a novel functional equation approach to the BES equation, facilitating strong coupling analysis and connecting to previous recursive solutions.

Findings

Successfully reformulated the BES equation as functional equations.

Perturbative strong coupling solutions match previous recursive results.

Coefficients are determined by analyticity properties of resolvents.

Abstract

We give a realization of the Beisert, Eden and Staudacher equation for the planar N=4 supersymetric gauge theory whichseems to be particularly useful to study the strong coupling limit. We use a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into to a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotanski. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.