Complex curve of the two-matrix model and its tau-function

Vladimir A. Kazakov, Andrei Marshakov

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)


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 N = 1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multi-matrix models with tree-like interactions is considered.

Original languageEnglish
Pages (from-to)3107-3136
Number of pages30
JournalJournal of Physics A: Mathematical and General
Issue number12 SPEC. ISS.
Publication statusPublished - 28 Mar 2003
Externally publishedYes


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