Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model

Oct, 1998
46 pages
e-Print:
Report number:
  • ITEP-TH-78-97

Citations per year

19992005201120172023012345
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 c<1c<1. 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) pp-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