Off-Shell Amplitudes in Two Dimensional String Field Theory

TL;DR

This paper introduces a regularization method for off-shell amplitudes in two-dimensional string field theory, ensuring finite results for certain divergent amplitudes by relating discrete states to off-shell states.

Contribution

It provides an explicit regularization procedure linking discrete and off-shell states in open string field theory, enabling well-defined off-shell amplitudes.

Findings

Finite 4-point amplitudes with divergent channels after regularization

Regularization relates discrete states to off-shell states

Procedure allows defining all amplitudes consistently

Abstract

In this note we present an explicit procedure for the regularization of tree level amplitudes involving discrete states, using open string field theory. We show that there is a natural correspondence between the discrete states and off--shell states, later acting as a regularized version of the former. A general off-shell state corresponds to several physical states. In order to obtain the well--defined $S$ matrix elements one has to choose representatives close but not equal to the desired values of external momenta. The procedure renders finite all $4$-point amplitudes with an even number of (naively) divergent channels even after the regularization is removed. The rest of the amplitudes can be defined by means of such regularization.