Divergence cancellation and loop corrections in string field theory on a plane wave background

We investigate the one-loop energy shift δE to certain two-impurity string states in light-cone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers which cancel between the cubic hamiltonian and quartic ``contact term''. Analyzing the impurity non-conserving channel we find that the non-perturbative (g22λ'1/2) contribution to δE/μ predicted in [33] is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an (g22λ') contribution. Exploiting the supersymmetry algebra, we present a form for the energy shift which appears to be manifestly convergent and free of non-perturbative terms. We use this form to argue that δE/μ receives (g22λ') contributions at every order in intermediate state impurities.