Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy

Abstract

Based on the dispersionless KP (dKP) theory, we give a comprehensive study of the topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space.

54 pages, Plain TeX. Figure could be obtained from Kodama

References in corpus (4)

• The Topological CP^1 Model and the Large-N Matrix Integral
• Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy
• The Moyal bracket and the dispersionless limit of the KP hierarchy
• On Dubrovin Topological Field Theories

Cited by in corpus (48)

• Solution of the dispersionless Hirota equations
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
• Block type symmetry of bigraded Toda Hierarchy
• Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type
• The extended $Z_N$-Toda hierarchy
• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies
• Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves
• Dispersionless bigraded Toda Hierarchy and its additional symmetry
• Integrable equations in nonlinear geometrical optics
• Classical R-matrix theory for bi-Hamiltonian field systems
• On the extended multi-component Toda hierarchy
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
• Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems
• Geometrical optics in nonlinear media and integrable equations
• On Kernel Formulas and Dispersionless Hirota Equations
• Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
• Sato theory on the $q$-Toda hierarchy and its extension
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• On the Benney Hierarchy: free energy, string equation and quantization
• The Whitham Deformation of the Dijkgraaf-Vafa Theory
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
• The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
• Recursion Operator and Rational Lax Representation
• Classical $r$-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics
• The constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources
• Nonlinear Beltrami equation and tau-function for dispersionless hierarchies
• On the water-bag model of dispersionless KP hierarchy
• On the water-bag model of dispersionless KP hierarchy (II)
• Integrable Quasiclassical Deformations of Cubic Curves
• Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations
• Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
• Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy
• Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy
• WDVV Equations, Darboux-Egoroff Metric and the Dressing Method
• Alternative dispersionless limit of N=2 supersymmetric KdV-type hierarchies
• Quasi-classical DBAR-dressing approach to the weakly dispersive KP hierarchy
• Topological Gravity with Non-Compact Matter
• Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation
• A Note on Symmetries of WDVV Equations
• Infinite-dimensional Frobenius Manifolds Underlying the Universal Whitham Hierarchy
• Regular solution and lattice miura transformation of bigraded Toda Hierarchy
• Kernel Formula Approach to the Universal Whitham Hierarchy
• A note on the extended dToda hierarchy