HCIZ integral and 2D Toda lattice hierarchy

Details HCIZ integral and 2D Toda lattice hierarchy HCIZ integral and 2D Toda lattice hierarchy

2002-02-28

arxiv.org/abs/math-ph/0202045v4

Nucl.Phys. B634 (2002) 417-432

Physics

Mathematical Physics

20 pages. various minor improvements/corrections

Scientific paper

The expression of the large $N$ Harish Chandra--Itzykson--Zuber (HCIZ) integral in terms of the moments of the two matrices is investigated using an auxiliary unitary two-matrix model, the associated biorthogonal polynomials and integrable hierarchy. We find that the large $N$ HCIZ integral is governed by the dispersionless Toda lattice hierarchy and derive its string equation. We use this to obtain various exact results on its expansion in powers of the moments.

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