Exact S-matrix for two-dimensional string theory

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.