Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model
Oct, 1998Citations per year
Abstract:
The review is devoted to the integrable properties of the Generalized Kontsevich Model which is supposed to be an universal matrix model to describe the conformal field theories with . It is shown that the deformations of the "monomial" phase to "polynomial" one have the natural interpretation in context of so-called equivalent hierarchies. The dynamical transition between equivalent integrable systems is exactly along the flows of the dispersionless Kadomtsev-Petviashvili hierarchy; the coefficients of the potential are shown to be directly related with the flat (quasiclassical) times arising in N=2 Landau-Ginzburg topological model. The Virasoro constraint for solution with an arbitrary potential is shown to be a standard \L_{-p}-constraint of the (equivalent) -reduced hierarchy with the times additively corrected by the flat coordinates.- review
- field theory: conformal
- Kontsevich model
- integrability
- potential
- partition function
- Kadomtsev-Petviashvili equation: hierarchy
- semiclassical
- Landau-Ginzburg model: topological
- algebra: Virasoro
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