Complex curve of the two-matrix model and its tau-function
Authors: Kazakov V.A.1; Marshakov A.1
Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3107-3136(30)
Publisher: Institute of Physics Publishing
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Abstract:
We study the Hermitian and normal two-matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one-matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be a quasiclassical tau-function. The relation to 1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multi-matrix models with tree-like interactions is considered.
Language: English
Document Type: Miscellaneous
Affiliations: 1: Laboratoire de Physique Théorique de l'Ecole Normale Supérieure4 footnote id"4" pos"affil": Unité mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l'Ecole Normale Supéerieure et à l'Université de Paris-Sud. /footnote: , 24 rue Lhomond, 75231 Paris Cedex, France
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