Time-dependent backgrounds of 2D string theory

TL;DR

This paper explores various time-dependent backgrounds in 2D string theory by analyzing fermionic systems and Toda lattice integrable structures, revealing connections to Sine-Liouville theory and electron droplets in magnetic fields.

Contribution

It introduces a novel approach to classify 2D string backgrounds via fermionic profiles and integrable flows, extending understanding of string perturbations and their mathematical structures.

Findings

Backgrounds correspond to fermionic Fermi sea profiles.

Perturbations generated by Toda lattice integrable flows.

Application to Sine-Liouville and electron droplet models.

Abstract

We study possible backgrounds of 2D string theory using its equivalence with a system of fermions in upside-down harmonic potential. Each background corresponds to a certain profile of the Fermi sea, which can be considered as a deformation of the hyperbolic profile characterizing the linear dilaton background. Such a perturbation is generated by a set of commuting flows, which form a Toda Lattice integrable structure. The flows are associated with all possible left and right moving tachyon states, which in the compactified theory have discrete spectrum. The simplest nontrivial background describes the Sine-Liouville string theory. Our methods can be also applied to the study of 2D droplets of electrons in a strong magnetic field.