Combinatorial Solution of the Two-Matrix Model

Details Combinatorial Solution of the Two-Matrix Model Combinatorial Solution of the Two-Matrix Model

1993-01-12

arxiv.org/abs/hep-th/9301038v1

Phys.Lett. B305 (1993) 332-338

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Rutgers preprint RU-92-64

Scientific paper

10.1016/0370-2693(93)91063-S

We write down and solve a closed set of Schwinger-Dyson equations for the two-matrix model in the large $N$ limit. Our elementary method yields exact solutions for correlation functions involving angular degrees of freedom whose calculation was impossible with previously known techniques. The result sustains the hope that more complicated matrix models important for lattice string theory and QCD may also be solvable despite the problem of the angular integrations. As an application of our method we briefly discuss the calculation of wavefunctions with general matter boundary conditions for the Ising model coupled to $2D$ quantum gravity. Some novel insights into the relationship between lattice and continuum boundary conditions are obtained.

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