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

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.

52 pages, Latex.

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Cited by in corpus (19)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Toda hierarchies and their applications
• Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation
• Fermionic representation for basic hypergeometric functions related to Schur polynomials
• Comments on 2D Type IIA String and Matrix Model
• Topological B-Model, Matrix Models, $\hat{c}=1$ Strings and Quiver Gauge Theories
• Generalized string equations for double Hurwitz numbers
• Tau Functions and Matrix Integrals
• Modified melting crystal model and Ablowitz-Ladik hierarchy
• Orbifold melting crystal models and reductions of Toda hierarchy
• Generalized Ablowitz-Ladik hierarchy in topological string theory
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Hypergeometric tau functions $\tau (\mathbf{t},T,{\mathbf{t}}^{\ast })$ as $\infty$-soliton tau function in T variables
• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
• Matrix Integrals, Symmetric Functions theory and matrix integrals
• Integrable structure of melting crystal model with external potentials
• Integrable structures of specialized hypergeometric tau functions
• Notes about KP/BKP correspondence
• Integrable Deformations of $\hat{c}=1$ Strings in Flux Backgrounds