Quantum and Classical Aspects of Deformed $c=1$ Strings.

TL;DR

This paper explores the quantum and classical features of a deformed $c=1$ string matrix model, analyzing its string equations within the Toda hierarchy and examining different perturbative interpretations and their effects on scattering amplitudes.

Contribution

It formulates string equations for the deformed $c=1$ matrix model using Toda hierarchy and investigates multiple perturbative interpretations and their impact on classical scattering amplitudes.

Findings

Whittaker functions act as generalized Airy functions in $c<1$ strings

Classical scattering amplitudes are insensitive to parameter deformations

Multiple perturbative interpretations of the model are possible

Abstract

The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in $c<1$ strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model.