KALUZA–KLEIN GAUGE AND MINIMAL INTEGRABLE EXTENSION OF OSp(4|6)/(SO(1, 3) × U(3)) SIGMA-MODEL

Abstract

Basing upon experience from performing double-dimensional reduction of the D = 11 supermembrane on AdS 4 × S7 background to Type IIA superstring on AdS 4 × ℂℙ3 we introduce Kaluza–Klein (partial) κ-symmetry gauge as a vanishing condition of the contributions to the D = 11 supervielbein components tangent to D = 10 space–time that are proportional to the differential of the coordinate parametrizing compact 11th space–time dimension identified with the supermembrane worldvolume compact dimension. For AdS 4 × S7 supermembrane Kaluza–Klein gauge removes half Grassmann coordinates associated with eight space–time supersymmetries, broken by the AdS 4 × ℂℙ3 superbackground, by imposing D = 3 (anti-)Majorana condition on them. The consideration relies on the realization of osp(4|8) isometry superalgebra of the AdS 4 × S7 superbackground as [Formula: see text] superconformal algebra. Requiring further vanishing of the D = 10 dilaton leaves in the sector of broken supersymmetries just two Grassmann coordinates organized into D = 3 (anti-)Majorana spinor that defines minimal SL(2, ℝ)-covariant extension of the OSp(4|6)/(SO(1, 3) × U(3)) sigma-model. Among four possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D = 3 Majorana coordinate related to broken Poincaré supersymmetry, and show that the AdS 4 × ℂℙ3 superstring equations of motion in this partial κ-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1, 3) × U(3)) sigma-model and the AdS 4 × ℂℙ3 superstring is revisited.