Multiloop Amplitudes of Light-cone Gauge NSR String Field Theory in Noncritical Dimensions

Abstract

Feynman amplitudes of light-cone gauge superstring field theory are ill-defined because of various divergences. In a previous paper, one of the authors showed that taking the worldsheet theory to be the one in a linear dilaton background $\Phi=-iQX^{1}$ with Feynman $i\varepsilon$ $(\varepsilon>0)$ and $Q^{2}>10$ yields finite amplitudes. In this paper, we apply this worldsheet theory to dimensional regularization of the light-cone gauge NSR superstring field theory. We concentrate on the amplitudes for even spin structure with external lines in the (NS,NS) sector. We show that the multiloop amplitudes are indeed regularized in our scheme and that they coincide with the results in the first-quantized formalism through the analytic continuation $Q\to0$.