Light-cone Gauge Superstring Field Theory and Dimensional Regularization II

TL;DR

This paper introduces a dimensional regularization scheme for light-cone gauge superstring field theory, enabling divergence control and reproducing known results without contact interactions by formulating the theory in arbitrary dimensions.

Contribution

It develops a dimensional regularization approach for superstring field theory in light-cone gauge, ensuring BRST invariance and matching first quantized results in the limit.

Findings

Dimensional regularization effectively manages divergences from colliding supercurrents.

Tree level amplitudes match first quantized theory results as dimension approaches 10.

No additional contact interactions are needed in the regularized formulation.

Abstract

We propose a dimensional regularization scheme to deal with the divergences caused by colliding supercurrents inserted at the interaction points, in the light-cone gauge NSR superstring field theory. We formulate the theory in $d$ dimensions and define the amplitudes as analytic functions of $d$. With an appropriately chosen three-string interaction term and large negative $d$, the tree level amplitudes for the (NS,NS) closed strings can be recast into a BRST invariant form, using the superconformal field theory proposed in Ref.[arXiv:0911.3704]. We show that in the limit $d \to 10$ they coincide with the results of the first quantized theory. Therefore we obtain the desired results without adding any contact interaction terms to the action.