Rational Theories of 2D Gravity from the Two-Matrix Model

Details Rational Theories of 2D Gravity from the Two-Matrix Model Rational Theories of 2D Gravity from the Two-Matrix Model

1993-03-16

arxiv.org/abs/hep-th/9303093v2

Nucl.Phys. B409 (1993) 311-338

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, preprint CERN-TH.6834/93

Scientific paper

10.1016/0550-3213(93)90582-A

The correspondence claimed by M. Douglas, between the multicritical regimes of the two-matrix model and 2D gravity coupled to (p,q) rational matter field, is worked out explicitly. We found the minimal (p,q) multicritical potentials U(X) and V(Y) which are polynomials of degree p and q, correspondingly. The loop averages W(X) and \tilde W(Y) are shown to satisfy the Heisenberg relations {W,X} =1 and {\tilde W,Y}=1 and essentially coincide with the canonical momenta P and Q. The operators X and Y create the two kinds of boundaries in the (p,q) model related by the duality (p,q) - (q,p). Finally, we present a closed expression for the two two-loop correlators and interpret its scaling limit.

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