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Basing upon experience from performing double-dimensional reduction of theD=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 xCP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishingcondition of the contribution to the D=11 supervielbein components tangent toD=10 space-time proportional to the differential of the coordinateparametrizing compact 11-th space-time dimension, that is identified with thesupermembrane world-volume compact dimension. For AdS_4 x S^7 supermembraneKaluza-Klein gauge removes half Grassmann coordinates associated with 8space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, byimposing D=3 (anti-)Majorana condition on them. The consideration relies on therealization of osp(4|8) isometry superalgebra of the AdS_4 x S^7superbackground as D=3 N=8 superconformal algebra. Requiring further vanishingof the D=10 dilaton leaves in the sector of broken supersymmetries just twoGrassmann coordinates organized into D=3 (anti-)Majorana spinor that definesminimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3))sigma-model. Among 4 possibilities of such a minimal extension we consider indetail one, that corresponds to picking out D=3 Majorana coordinate related tobroken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstringequations of motion in this partial kappa-symmetry gauge are integrable. Alsothe relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 xCP^3 superstring is revisited.

Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model