Unified description of correlators in non-Gaussian phases of Hermitean matrix model

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of non-Gaussian phases of the Hermitean one-matrix model. A unified approach is proposed for description of “connected correlators” in the form of the phaseindependent “check-operators” acting on the small space of T -variables (which parameterize the polynomialW (z)). With appropriate definitions and ordering prescriptions, the multidensity checkoperators look very similar to the Gaussian case (however, a reliable proof of suggested explicit expressions in all loops is not yet available, only certain consistency checks are performed).