Tachyon Backgrounds in 2D String Theory

TL;DR

This paper investigates tachyonic backgrounds in 2D string theory, specifically the Sine-Liouville background, and demonstrates the equivalence of two different analytical approaches through explicit Fermi surface construction.

Contribution

It shows the equivalence of collective field theory and Toda integrable systems approaches in analyzing tachyon backgrounds in 2D string theory.

Findings

The two methods yield the same Fermi surface structure.

Deformation of the potential in Toda systems matches collective field results.

Explicit comparison confirms the approaches are equivalent.

Abstract

We consider the construction of tachyonic backgrounds in two-dimensional string theory, focusing on the Sine-Liouville background. This can be studied in two different ways, one within the context of collective field theory and the other via the formalism of Toda integrable systems. The two approaches are seemingly different. The latter involves a deformation of the original inverted oscillator potential while the former does not. We perform a comparison by explicitly constructing the Fermi surface in each case, and demonstrate that the two apparently different approaches are in fact equivalent.