Dispersionless Toda hierarchy and two-dimensional string theory

Abstract

The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of ``extra'' states and fields are presented.

LaTeX 21 pages, KUCP-0067 (typos are corrected and a brief note is added)

References in corpus (14)

• Algebraic Structures and Differential Geometry in 2D String Theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• SDiff(2) KP hierarchy
• The partition function of 2d string theory
• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Quasi-classical limit of Toda hierarchy and W-infinity symmetries
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• Topological Strings, Flat Coordinates and Gravitational Descendants
• Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States
• Topological Landau-Ginzburg Formulation and Integrable Structure of 2d String Theory
• Ward Identities in Two-Dimensional String Theory
• Topological Field Theories and the Period Integrals
• The Master Equation of 2D String Theory
• Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

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• Toda Lattice Hierarchy and Generalized String Equations
• Toda hierarchies and their applications
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• Quantum and Classical Aspects of Deformed $c=1$ Strings.
• Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
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• Generalized string equations for double Hurwitz numbers
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• Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit
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• Conformal Mappings and Dispersionless Toda hierarchy II: General String Equations
• Solutions of the Dispersionless Toda Hierarchy Constrained by String Equations
• Conformal Mappings and Dispersionless Toda hierarchy
• Topological Field Theory Interpretations and LG Representation of c=1 String Theory
• On the dispersionless Davey-Stewartson hierarchy: Zakharov-Shabat equations, twistor structure and Lax-Sato formalism
• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
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• On dispersionless coupled modified KP hierarchy
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• Integrable structure of melting crystal model with external potentials
• c=1 discrete states correlators via W${}_{1+\infty }$ constraints
• Remarks on the waterbag model of dispersionless Toda Hierarchy
• Non-degenerate solutions of universal Whitham hierarchy
• Integrable Deformations of $\hat{c}=1$ Strings in Flux Backgrounds
• Integrable semi-discretization of complex and multi-component coupled dispersionless systems and their solutions
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