Light cone superstrings in AdS space

We discuss light-cone gauge description of type IIB Green-Schwarz superstri ng in AdS(5) x S-5 with a hope to make progress towards understanding spect rum of this theory. As in flat space, fixing light-cone gauge consists of t wo steps: (i) fixing kappa symmetry in such a way that the fermionic part o f the action does not depend on x(-); (ii) fixing 2-d reparametrizations by x(+) = tau and a condition on 2-d metric. In curved AdS space the latter c annot be the standard conformal gauge and breaks manifest 2-d Lorentz. inva riance. It is natural, therefore, to work in phase-space framework, imposin g the GGRT light-cone gauge conditions x(+) = tau, P+ =const. We obtain the resulting light-cone superstring Hamiltonian.