Classical Scattering in $1+1$ Dimensional String Theory

TL;DR

This paper solves classical scattering equations in 1+1 dimensional string theory, enabling efficient amplitude calculations, mapping backgrounds to sigma models, and deriving recursion relations for tachyon amplitudes.

Contribution

It provides the general solution to classical scattering equations, facilitating amplitude computations and background mappings in 1+1D string theory.

Findings

Explicit solution to scattering equations

Efficient amplitude computation in Liouville background

Recursion relations for tachyon amplitudes

Abstract

We find the general solution to Polchinski's classical scattering equations for $1+1$ dimensional string theory. This allows efficient computation of scattering amplitudes in the standard Liouville $\times$ $c=1$ background. Moreover, the solution leads to a mapping from a large class of time-dependent collective field theory backgrounds to corresponding nonlinear sigma models. Finally, we derive recursion relations between tachyon amplitudes. These may be summarized by an infinite set of nonlinear PDE's for the partition function in an arbitrary time-dependent background.