Non-linear integral equations in {\cal {N}}=4 SYM

TL;DR

This paper reviews the use of non-linear integral equations derived from Bethe Ansatz methods to analyze the eigenvalues of the dilatation operator in ${ m extbf{N}}=4$ SYM, including a novel derivation approach.

Contribution

It introduces a new method for deriving non-linear integral equations related to the spectral problem in ${ m extbf{N}}=4$ SYM, expanding on existing techniques.

Findings

Survey of applications of non-linear integral equations in ${ m extbf{N}}=4$ SYM

Introduction of a novel derivation method for these equations

Discussion of implications for the eigenvalues of the dilatation operator

Abstract

We survey and discuss the applications of the non-linear integral equation in the framework of the Bethe Ansatz type equations which are conjectured to give the eigenvalues of the dilatation operator in ${\cal {N}}=4$ SYM. Moreover, an original idea (different from that of \cite {FMQR}) to derive a non-linear integral equation is briefly depicted in Section 4.