GSO(-) Vertex Operators and Open Superstring Field Theory in Hybrid Variables

We consider the $GSO(-)$ sector of the open superstring using the formalism with four-dimensional hybrid variables. This sector is defined by the world sheet hybrid variables $(\theta^{\alpha},\bar{\theta}^{\dot\alpha})$ with antiperiodic boundary conditions. The corresponding spectrum of states and conditions for physical vertices are described. In particular we construct explicitly the lower level $GSO(-)$ vertex operators corresponding to the tachyon and the massless fermions. Using these new vertices, the tachyon and massless sector contribution to the superstring field theory action of Berkovits is evaluated. In this way we have included the Ramond sector and we end by discussing some features of the action