2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
arXiv:hep-th/0502041 · doi:10.1007/s00220-006-1541-8
Abstract
We prove that the 2-hermitean matrix model and the complex-matrix model obey the same loop equations, and as a byproduct, we find a formula for Itzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) are rewritten as gaussian integrals over triangular matrices and then computed explicitly. That formula is an efficient alternative to the former Shatashvili's formula.
29 pages, Latex
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- BPS coherent states and localization
- Mixed correlation function and spectral curve for the 2-matrix model
- Some properties of angular integrals
- Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
- Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics
- On character expansion and Gaussian regularization of Itzykson-Zuber measure
- Vogel's universality and the classification problem for Jacobi identities
- Itzykson-Zuber correlators from character expansion