Evidence for the classical integrability of the complete AdS4 x CP3 superstring

We construct a zero-curvature Lax connection in a sub-sector of the super-string theory on AdS(4) x CP3 which is not described by the OSp(6 vertical bar 4)/U(3) x SO(1, 3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z(4)-automorphism of the isometry superalgebra OSp(6 vertical bar 4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.