On integrability of classical superstrings in AdS 5 × S 5

We explore integrability properties of superstring equations of motion in AdS 5 × S 5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS 3 × S 3 and AdS 3 × S 1 subsectors containing both bosonic and fermionic fields. © SISSA 2005