Macroscopic loop amplitudes in the multi-cut two-matrix models

Abstract

Multi-cut critical points and their macroscopic loop amplitudes are studied in the multi-cut two-matrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and potentials in the multi-cut matrix models, we calculate the macroscopic loop amplitudes in the Z_k symmetric background. With a natural large N ansatz for the matrix Lax operators, a sequence of new solutions for the amplitudes in the Z_k symmetric k-cut two-matrix models are obtained, which are realized by the Jacobi polynomials.

46 pages, 3 figures; v2: 51 pages, 7 figures, notations changed, explanations in Section 2.4 extended, figures for topology of the curves added, Appendix E added, final version to appear in Nucl. Phys. B

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• Notes on the algebraic curves in (p,q) minimal string theory
• Fractional supersymmetric Liouville theory and the multi-cut matrix models
• Notes on D-branes and dualities in (p,q) minimal superstring theory

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• Duality Constraints on String Theory: Instantons and spectral networks
• Wronskians, dualities and FZZT-Cardy branes