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

We investigate the one-loop energy shift delta E 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 O(g(2)(2)root lambda') contribution to delta E/mu predicted in [33] is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an O(g(2)(2)lambda') 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 delta E/mu receives O(g(2)(2)lambda') contributions at every order in intermediate state impurities.