Vacuum solutions in the Neveu–Schwarz field theory of a fermionic string and the zero-curvature representation in graded spaces

We demonstrate that vacuum solutions in the Neveu–Schwarz field theory of a fermionic string incorporating the GSO$(-)$ sector are naturally related to the zero-curvature representation in a graded space of special form. We use the same representation to describe the equivalence of the cubic and nonpolynomial theories with the GSO$(-)$ sector also taken into account.