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

TL;DR

This paper studies one-loop energy corrections in string field theory on a plane wave background, revealing divergence cancellations and clarifying the nature of non-perturbative contributions, with implications for the structure of energy shifts.

Contribution

It demonstrates divergence cancellations between Hamiltonian terms and refines the understanding of non-perturbative effects in string field theory on a plane wave background.

Findings

Logarithmic divergences cancel between cubic and quartic terms.

Non-perturbative order g_2^2 sqrt(lambda') contributions vanish.

Order g_2^2 lambda' corrections appear at all impurity levels.

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.