Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

TL;DR

This paper demonstrates the classical integrability of a specific sector of the AdS(4) x CP(3) superstring by constructing a Lax connection that accounts for fermions associated with broken supersymmetries, extending previous methods.

Contribution

It introduces an alternative approach to construct the Lax connection for a non-supercoset sector of the superstring, incorporating broken supersymmetries.

Findings

Constructed a zero-curvature Lax connection for a non-supercoset sector.

Extended integrability proof beyond the supercoset sigma-model.

Demonstrated the method's reliance on target space isometry and kappa-symmetry.

Abstract

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|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|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.