On Time-Dependent Backgrounds In 1+1 Dimensional String Theory

TL;DR

This paper investigates time-dependent backgrounds in 1+1 dimensional string theory where standard asymptotic observables like the S-matrix may not exist, analyzing scattering, particle production, and fermion dynamics in these evolving geometries.

Contribution

It provides a detailed analysis of backgrounds with a Liouville wall that becomes spacelike, exploring the implications for scattering and the dynamics of free fermions in such settings.

Findings

Scattering amplitudes are computed where the Liouville wall remains timelike.

The continuation of scattering processes into spacelike regimes is discussed.

The fermion dynamics reveal insights into the time-dependent backgrounds.

Abstract

In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1+1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.