Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-11-25
J.Phys.A36:3107-3136,2003
Physics
High Energy Physics
High Energy Physics - Theory
36 pages, 10 figures, TeX; final version appeared in special issue of J.Phys. A on Random Matrix Theory
Scientific paper
10.1088/0305-4470/36/12/315
We study the hermitean 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 the quasiclassical tau-function. The relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multimatrix models with tree-like interactions is considered.
Kazakov Vladimir A.
Marshakov Andrei
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