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

TL;DR

This paper demonstrates that multiloop amplitudes in light-cone gauge NSR string field theory, regularized via a linear dilaton background, are finite and match first-quantized results through analytic continuation.

Contribution

It introduces a dimensional regularization scheme using a linear dilaton background to make multiloop amplitudes finite in noncritical dimensions.

Findings

Multiloop amplitudes are regularized and finite.

Results match first-quantized formalism after analytic continuation.

Scheme applies to even spin structure with (NS,NS) external lines.

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 $Q\to0$.