A Note on Cubic Interactions in PP-Wave Light Cone String Field Theory

TL;DR

This note reexamines pp-wave light-cone string field theory and resolves the puzzle between supergravity Neumann matrices and the zero-mode sector by identifying nonzero overlap with excited modes as the source of mismatch; it demonstrates that the zero-mode decoupling is not exact at finite μ and presents the μ-dependent ratio R with known asymptotics, restoring agreement in the μ→0 limit. It reevaluates the role of the prefactor, showing it corresponds to the energy difference between cos and sin mode sectors rather than the total energy difference, affecting how interactions are interpreted. It further argues that energy non-preserving amplitudes cannot be captured by perturbative large-N gauge theory and likely require non-perturbative effects, with non-perturbative physics becoming relevant for these processes, while consistency is recovered in the flat-space limit.

Abstract

We study the string modes in the pp-wave light-cone string field theory. First, we clarify the discrepancy between the Neumann coefficients for the supergravity vertex and the zero mode of the full string one. We also repeat our previous manipulation of the prefactor for the string modes and find that the prefactor reduces to the energy difference of the cos modes minus that of the sin modes. Finally, we discuss off-shell three-string processes.