Scattering of Discrete States in Two Dimensional Open String Field Theory

TL;DR

This paper investigates the interactions of discrete states and tachyons in two-dimensional open string field theory, analyzing four-point amplitudes and the conditions leading to divergences in correlation functions.

Contribution

It clarifies the origin and role of discrete physical states and examines their interactions with tachyons, providing explicit examples and conformal checks.

Findings

Correlation functions depend on the number of tachyons and kinematic invariants.

Divergences occur when certain invariants are non-positive integers.

Explicit examples illustrate the behavior of amplitudes and divergences.

Abstract

This is the second in a series of papers devoted to open string field theory in two dimensions. In this paper we aim to clarify the origin and the role of discrete physical states in the theory. To this end, we study interactions of discrete states and generic tachyons. In particular, we discuss at length four point amplitudes. We show that behavior of the correlation functions is governed by the number of generic tachyons involved and values of the kinematic invariants $s$, $t$ and $u$. Divergence of certain classes of correlators is shown to be the consequence of the fact certain kinematic invariants are non--positive integers in that case. Explicit examples are included. We check our results by standard conformal technique.