Macroscopic loop amplitudes in the multi-cut two-matrix models. (English) Zbl 1203.81133
Summary: 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 \({\mathbb Z}_k\) symmetric background. With a natural large \(N\) ansatz for the matrix Lax operators, a sequence of new solutions for the amplitudes in the \({\mathbb Z}_k\) symmetric \(k\)-cut two-matrix models are obtained, which are realized by the Jacobi polynomials.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
Daul-Kazakov-Kostov prescriptionReferences:
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