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We study the structure of the normal matrix model (NMM). We show that allcorrelation functions of the model with axially symmetric potentials can beexpressed in terms of holomorphic functions of one variable. This observationis used to demonstrate the exact solvability of the model. The two-pointcorrelation function is calculated in the scaling limit by solving the BBGKYchain of equations. The answer is shown to be universal (i.e. potentialindependent up to a change of the scale). We then develop a two-dimensionalfree fermion formalism and construct a family of completely integrablehierarchies (which we call the extended-KP(N) hierarchies) of non-lineardifferential equations. The well-known KP hierarchy is a lower-dimensionalreduction of this family. The extended-KP(1) hierarchy contains the(2+1)-dimensional Burgers equations. The partition function of the N*N NMM isthe tau function of the extended-KP(N) hierarchy invariant with respect to asubalgebra of an algebra of all infinitesimal diffeomorphisms of the plane.Comment: 43 pages, no figure

On the Structure of Correlation Functions in the Normal Matrix Model