Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

TL;DR

This paper introduces a universal integrable hierarchy for D-type topological Landau-Ginzburg models, revealing a structure with positive and negative flows and linking solutions to a Riemann-Hilbert problem.

Contribution

It presents a new integrable hierarchy underlying D-type topological Landau-Ginzburg models, including a characterization of solutions via a Riemann-Hilbert problem and a generalized hodograph transformation.

Findings

Hierarchy has positive and negative flow sets.

Special solutions are characterized by a Riemann-Hilbert problem.

Embedding of finite phase space into the hierarchy's flow space.

Abstract

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation. This construction gives an embedding of the finite dimensional small phase space of these models into the full space of flows of this hierarchy. One of flat coordinates in the small phase space turns out to be identical to the first ``negative" time variable of the hierarchy, whereas the others belong to the ``positive" flows.