Time-dependent backgrounds of two dimensional string theory from the $c=1$ matrix model

TL;DR

This paper explores time-dependent backgrounds in two-dimensional string theory using the $c=1$ matrix model, analyzing fluctuations and tachyon fields for lightlike and spacelike boundaries, including novel spacelike boundary cases.

Contribution

It establishes a correspondence between matrix model solutions and coupled dilaton-gravity, deriving fluctuations and tachyon fields for new spacelike boundary backgrounds.

Findings

Derived incoming and outgoing fluctuations for time-dependent backgrounds.

Mapped matrix model solutions to string theory tachyon fields.

First analysis of spacelike boundary backgrounds in this context.

Abstract

The aim of this paper is to use correspondence between solutions in the $c=1$ matrix model collective field theory and coupled dilaton-gravity to a massless scalar field. First, we obtain the incoming and outgoing fluctuations for the time-dependent backgrounds with the lightlike and spacelike boundaries. In the case of spacelike boundaries, we have done here for the first time. Then by using the leg-pole transformations we find corresponding tachyon field in two dimensional string theory for lightlikes and spacelikes boundary.