Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background

Abstract

We investigate the one-loop energy shift 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, order g_2^2 sqrt(lambda') contribution to E/mu predicted in hep-th/0211220 is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an order 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 E/mu receives order g_2^2 lambda' contributions at every order in intermediate state impurities.

27 pages; added references, acknowledgments, missing normalization in equations 2.3 - 2.8, also cleaned up notation, and added a few footnotes

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• New Penrose Limits and AdS/CFT
• Three-point functions of BMN operators at weak and strong coupling II. One loop matching
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