Correlation numbers in Minimal Liouville gravity from Douglas string equation
Mon, Nov. 04th 2013, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
I am going to present a review of some results of the joint works with my colleagues about so-called (p,q) Minimal Liouville gravity.I will argue that the generating function of the correlatorsin genus zero in Minimal Liouville gravity (MLG) is nothing butlogarithm of the Sato tau-function for dispersionless Gefand-Dikii hierarchy with the special initial condition given by Douglas string equation. But the correlators of Minimal Liouville gravity are not equal to the expansion coefficients of log of the tau-function in respect to KdV times $t_k$ near $t_k=0,if k>0$ like it is in Matrix models of 2d gravity. Instead the correlators of MLG are the expansion coefficients of Log of the tau-function in respect to the new variables connected with
KdV variables by a special noliniear "resonance" transformation. These correlators of MLG satisfy to the necessary conformal
and fusion rules as it should be M(p/q) conformal minimal models. We will use the connection between Minimal Liouville gravity and Frobenius manifolds to get an explicit and useful expression for log Sato tau-function corresponding Douglas string equation in dispersionless limit.