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

Abstract

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.

24 pages, preprint CERN-TH.6834/93

References in corpus (8)

• Multicritical Phases of the O(n) Model on a Random Lattice
• The $O(n)$ model on a random surface: critical points and large order behaviour
• Strings with Discrete Target Space
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Loop Gas Model for Open Strings
• From Virasoro Constraints in Kontsevich's Model to $\mathcal{W}$-constraints in 2-matrix Models
• Large Order Behaviour of 2D Gravity Coupled to $d<1$ Matter
• D-dimensional Induced Gauge Theory as a Solvable Matrix Model

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