Topological Strings with Scaling Violation and Toda Lattice Hierarchy

Abstract

We show that there is a series of topological string theories whose integrable structure is described by the Toda lattice hierarchy. The monodromy group of the Frobenius manifold for the matter sector is an extension of the affine Weyl group $\tilde{W}(A_N^{(1)})$ introduced by Dubrovin. These models are generalizations of the topological $C{P}^1$ string theory with scaling violation. The logarithmic Hamiltonians generate flows for the puncture operator and its descendants. We derive the string equation from the constraints on the Lax and the Orlov operators. The constraints are of different type from those for the $c=1$ string theory. Higher genus expansion is obtained by considering the Lax operator in matrix form.

27 pages, latex, no figures

References in corpus (13)

• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• The Topological CP^1 Model and the Large-N Matrix Integral
• SDiff(2) KP hierarchy
• Two dimensional black-hole as a topological coset model of c=1 string theory
• The partition function of 2d string theory
• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Topological Landau-Ginzburg Formulation and Integrable Structure of 2d String Theory
• Toda Lattice Hierarchy and the Topological Description of the c=1 String Theory
• Topological Field Theories and the Period Integrals
• Topological Landau-Ginzburg Model of Two-Dimensional String Theory
• Integrable hierarchy underlying topological Landau-Ginzburg models of D-type
• c=1 String Theory as a Topological G/G Model
• On the string equation at $c=1$

Cited by in corpus (5)

• Toda Lattice Hierarchy and Generalized String Equations
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
• On the Benney Hierarchy: free energy, string equation and quantization
• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
• Non Scale-Invariant Topological Landau-Ginzburg Models