On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory

TL;DR

This paper studies the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory, providing perturbative energy expansions in weak and strong coupling regimes and exploring its string theory analog.

Contribution

It identifies the highest-energy state as an operator analogous to the antiferromagnetic state and derives its energy behavior using Bethe ansatz methods.

Findings

Perturbative energy expansions in weak coupling

Perturbative energy expansions in strong coupling

Discussion of potential string theory analog

Abstract

We consider the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z is a complex scalar and \psi is a component of gaugino. We show that this state corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the antiferromagnetic state in the su(2) sector. We find perturbative expansions of the energy of this state in both weak and strong 't Hooft coupling regimes using asymptotic gauge theory Bethe ansatz equations. We also discuss a possible analog of this state in the conjectured string Bethe ansatz equations.