Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors

TL;DR

This paper derives integral equations for the highest states in su(1|1) and su(2) sectors of N=4 super Yang-Mills theory, solving them to find anomalous dimensions at weak and strong coupling.

Contribution

It constructs and solves integral equations from Bethe ansatz for highest states, providing analytic results across coupling regimes.

Findings

Derived integral equations for highest states.

Obtained weak coupling anomalous dimensions.

Analyzed strong coupling limit analytically.

Abstract

We construct the integral equations by taking the thermodynamic limit of both the all-loop gauge Bethe ansatz equation and the string Bethe ansatz equation for the highest states in the su(1|1) and su(2) sectors of the N=4 super Yang-Mills theory. Using the Fourier transformation we solve the integral equations iteratively to obtain the anomalous dimensions of the highest states in the weak coupling expansion. In the su(1|1) sector we analytically study the strong coupling limit of the anomalous dimension for the all-loop gauge Bethe ansatz equation by means of the Laplace transformation.