Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-11-13
Commun.Math.Phys. 196 (1998) 203-247
Physics
High Energy Physics
High Energy Physics - Theory
43 pages, no figures
Scientific paper
10.1007/s002200050420
We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with axially symmetric potentials can be expressed in terms of holomorphic functions of one variable. This observation is used to demonstrate the exact solvability of the model. The two-point correlation function is calculated in the scaling limit by solving the BBGKY chain of equations. The answer is shown to be universal (i.e. potential independent up to a change of the scale). We then develop a two-dimensional free fermion formalism and construct a family of completely integrable hierarchies (which we call the extended-KP(N) hierarchies) of non-linear differential equations. The well-known KP hierarchy is a lower-dimensional reduction of this family. The extended-KP(1) hierarchy contains the (2+1)-dimensional Burgers equations. The partition function of the N*N NMM is the tau function of the extended-KP(N) hierarchy invariant with respect to a subalgebra of an algebra of all infinitesimal diffeomorphisms of the plane.
Chau Ling-Lie
Zaboronsky Oleg
No associations
LandOfFree
On the structure of Normal Matrix Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the structure of Normal Matrix Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the structure of Normal Matrix Model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-464348