Matrix Model and Time-like Linear Dilaton Matter

TL;DR

This paper develops a matrix model for 2d string theory with a time-like linear dilaton matter, demonstrating agreement with world-sheet calculations and exploring the ground ring structure and D-brane dynamics.

Contribution

It introduces a matrix model description for the c=1 string theory with time-like linear dilaton matter, linking it to a deformed fermi surface and classical fermion trajectories.

Findings

Tree level scattering amplitudes match between matrix model and world-sheet theory.

Classical fermion trajectories correspond to decaying D-branes.

Ground ring structure resembles that of minimal string theory.

Abstract

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dilaton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-branes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string.