TY - JOUR

T1 - Complex curve of the two-matrix model and its tau-function

AU - Kazakov, Vladimir A.

AU - Marshakov, Andrei

PY - 2003/3/28

Y1 - 2003/3/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037471307&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/12/315

DO - 10.1088/0305-4470/36/12/315

M3 - Article

AN - SCOPUS:0037471307

VL - 36

SP - 3107

EP - 3136

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 12 SPEC. ISS.

ER -