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

Abstract

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-type is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (‘positive’ and ‘negative’) sets 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.