Lagrangian mechanics of massless superparticle on AdS4×CP3 superbackground

Massless superparticle model is considered on the OSp(4|6)/(SO(1,3)×U(3)) supercoset manifold and in the AdS4×CP3 superspace. In the former case integrability of the equations of motion is rather obvious, while for the AdS4×CP3 superparticle we prove integrability in the partial κ-symmetry gauge for which 4 anticommuting coordinates related to the broken conformal supersymmetry are set to zero. This allows us to propose expression for the Lax pair that may encode complete equations of motion for the AdS4×CP3 superparticle.