Highest states in light-cone AdS5 x S5 superstring

We study the highest states in the compact rank-1 sectors of the AdS5 x S5 superstring in the framework of the recently proposed light cone Bethe Ansatz equations. In the su(1 vertical bar 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 su(2) sector we perform the strong coupling expansions in the L → ∞ limit up to O(λ-1/4), and our result is in agreement with previuos String Bethe Ansatz analysis