Amplitudes in Noncritical Dimensions and Dimensional Regularization

TL;DR

This paper explores the use of dimensional regularization in light-cone gauge string field theory, demonstrating its effectiveness at tree level and confirming modular invariance of one-loop amplitudes in noncritical dimensions.

Contribution

It shows that contact terms are unnecessary as counter terms in this regularization at tree level and verifies modular invariance of one-loop amplitudes.

Findings

Contact terms are not needed at tree level in this regularization.

One-loop amplitudes in noncritical dimensions are modular invariant.

Dimensional regularization is effective in light-cone gauge string theory.

Abstract

We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the tree level. We also investigate the one-loop amplitudes of the bosonic theory in noncritical dimensions and show that they are modular invariant.