Note on cubic interactions inpp-wave light cone string field theory

We study the string modes in $\mathrm{pp}$-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 impurity number nonpreserving three-string processes.