More comments on superstring interactions in the pp-wave background

We reconsider light-cone superstring field theory on the maximally supersymmetric pp-wave background. We find that the results for the fermionic Neumann matrices given so far in the literature are incomplete and verify our expressions by relating them to the bosonic Neumann matrices and proving several non-trivial consistency conditions among them, as for example the generalization of a at space factorization theorem for the bosonic Neumann matrices. We also study the bosonic and fermionic constituents of the prefactor and point out a subtlety in the relation between continuum and oscillator basis expressions. We prove that if one requires the vertex to have an exponential form, the use of a different fermionic zero-mode vertex leads to inconsistencies not visible in supergravity.