Abstract
We study the highest states in the compact rank-1 sectors
of the AdS5 × S5 superstring in the framework of the recently proposed
light cone Bethe Ansatz equations. In the 
(1|1) sector
we present strong coupling expansions in the two limits L,λ→∞ (expanding in power of λ−1/4 with fixed
large L) and λ,L → ∞ (expanding in power of 1/L with
fixed large λ) where λ is the 't Hooft coupling and
L is the number of Bethe momenta. The two limits do not commute
apart from the leading term which reproduces the result obtained with
the Arutyunov-Frolov-Staudacher phase in the λ,L → ∞
limit. In the (2) sector we perform the strong coupling
expansions in the L → ∞ limit up to 
(λ−1/4),
and our result is in agreement with previuos String Bethe Ansatz analysis.
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