Exact S-Matrix for 2D String Theory

TL;DR

This paper develops graphical rules for calculating nonperturbative $c=1$ $S$-matrices in 2D string theory, revealing an infinite family of unitary solutions and analyzing their analytic and high-energy properties.

Contribution

It introduces a simple graphical method for explicit nonperturbative $S$-matrix calculations and explores the space of unitary solutions in 2D string theory.

Findings

Existence of an infinite parameter family of nonperturbatively unitary $c=1$ $S$-matrices.

Identification of resonant behavior at high energies and in the complex energy plane.

Analysis of the dependence of the $S$-matrix on nonperturbative parameters.

Abstract

We formulate simple graphical rules which allow explicit calculation of nonperturbative $c=1$ $S$-matrices. This allows us to investigate the constraint of nonperturbative unitarity, which indeed rules out some theories. Nevertheless, we show that there is an infinite parameter family of nonperturbatively unitary $c=1$ $S$-matrices. We investigate the dependence of the $S$-matrix on one of these nonperturbative parameters. In particular, we study the analytic structure, background dependence, and high-energy behavior of some nonperturbative $c=1$ $S$-matrices. The scattering amplitudes display interesting resonant behavior both at high energies and in the complex energy plane.