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

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.