Topological Strings with Scaling Violation and Toda Lattice Hierarchy

Details Topological Strings with Scaling Violation and Toda Lattice Hierarchy Topological Strings with Scaling Violation and Toda Lattice Hierarchy

1995-02-06

arxiv.org/abs/hep-th/9502029v1

Nucl.Phys.B442:179-204,1995

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, latex, no figures

Scientific paper

10.1016/S0550-3213(95)00138-7

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 $\widetilde W (A_N^{(1)})$ introduced by Dubrovin. These models are generalizations of the topological $CP^1$ 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.

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