More comments on superstring interactions in the pp-wave background

TL;DR

This paper refines the light-cone superstring field theory on the maximally supersymmetric pp-wave background by correcting the fermionic Neumann matrices, linking them to the bosonic sector, and establishing consistency via a pp-wave generalization of the flat-space factorization theorem. It then analyzes the prefactor, detailing both its bosonic and fermionic components, and shows a nontrivial μ-dependent normalization governs the fermionic continuum-oscillator mapping. The results are checked against the μ→0 flat-space limit, where they reproduce the Green-Schwarz–Brink framework, bolstering confidence in pp-wave string interactions. Overall, the work strengthens the understanding of string interactions in the pp-wave background and clarifies the subtleties arising in the fermionic sector.

Abstract

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 flat 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.