Light-cone superstring in AdS space-time

We consider fixing the bosonic light-cone gauge for string in AdS space in the phase space framework, i.e., by choosing x(+) = tau, and by choosing a so that p(+) is distributed uniformly (its density p(+) is independent of sigma). We discuss classical bosonic string in AdS(d) and superstring in AdS(5) x S-5. In the latter case the starting point is the action found in hep-th/0007036, where the K-symmetry is fixed by a fermionic light-cone type gauge. We derive the light-cone Hamiltonian in the AdS5 x S5 case and in the case of superstring in AdS(3) x S-3. We also obtain a realization of the generators of the basic superalgebra psu(2, 2\4) in terms of AdS(5) x S5 superstring coordinate 2-d fields in the light-cone gauge. (C) 2001 Elsevier Science B.V. All rights reserved.