Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-10-13
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 46 pp
Scientific paper
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 $c<1$. 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) $p$-reduced hierarchy with the times additively corrected by the flat coordinates.
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