Complete type IIA superstring action on IIA plane wave background

TL;DR

This paper constructs the complete type IIA superstring action on a plane wave background, maintaining all fermionic degrees of freedom, and demonstrates its consistency with known gauge-fixed actions.

Contribution

It provides the full Green-Schwarz superstring action on a IIA plane wave background with all fermions, derived via superalgebra and Kaluza-Klein reduction, extending previous partial results.

Findings

Full superstring action with 32 fermions constructed.

Action reduces to known light-cone gauge fixed form.

Derived from eleven-dimensional superalgebra and reduction.

Abstract

We construct the type IIA Green-Schwarz superstring action on a ten-dimensional IIA plane wave background with 24 supersymmetries keeping the full 32 fermionic coordinates. Starting from the symmetry superalgebra for the maximally supersymmetric eleven dimensional plane wave background, we obtain the eleven dimensional superfields. The Kaluza-Klein reduction leads to the ten dimensional superfields for the IIA plane wave background, from which the type IIA superstring action is constructed. We show that the superstring action reduces correctly to the previously known light-cone gauge fixed action upon imposing the light-cone $\kappa$-symmetry fixing condition.