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

TL;DR

This paper introduces a new gauge fixing method for supermembranes in AdS_4 x S^7, leading to a minimal integrable sigma-model extension of the AdS_4 x CP^3 superstring, with implications for understanding supersymmetry breaking.

Contribution

It proposes a novel Kaluza-Klein gauge fixing that simplifies the supermembrane description and constructs a minimal integrable sigma-model extension of the superstring in AdS_4 x CP^3.

Findings

The gauge removes half of the Grassmann coordinates associated with broken supersymmetries.

The resulting sigma-model is shown to be integrable.

The relation between the sigma-model and superstring equations of motion is clarified.

Abstract

Basing upon experience from performing double-dimensional reduction of the D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing condition of the contribution to the D=11 supervielbein components tangent to D=10 space-time proportional to the differential of the coordinate parametrizing compact 11-th space-time dimension, that is identified with the supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane Kaluza-Klein gauge removes half Grassmann coordinates associated with 8 space-time supersymmetries, broken by the AdS_4 x CP^3 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 x S^7 superbackground as D=3 N=8 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)x U(3)) sigma-model. Among 4 possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D=3 Majorana coordinate related to broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring equations of motion in this partial kappa-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x CP^3 superstring is revisited.