New Scaling of Itzykson-zuber Integrals
نویسندگان
چکیده
ABSTRACT. We study asymptotics of the Itzykson-Zuber integrals in the scaling when one of the matrices has a small rank compared to the full rank. We show that the result is basically the same as in the case when one of the matrices has a fixed rank. In this way we extend the recent results of Guionnet and Maı̈da who showed that for a latter scaling the Itzykson-Zuber integral is given in terms of the Voiculescu’s R– transform of the full rank matrix.
منابع مشابه
1 v 3 1 9 Ju n 20 01 Character Expansions , Itzykson - Zuber Integrals , and the QCD Partition Function
A combinatorial formula to generate U (N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of ...
متن کاملUnitary Integrals and Related Matrix Models
Concise review of the basic properties of unitary matrix integrals. They are studied with the help of the three matrix models: the ordinary unitary model, Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model. Especial attention is paid to the tricky sides of the story, from De Wit-t’Hooft anomaly in unitary integrals to the problem of correlators with Itzykson-Zuber measure. O...
متن کامل3 New solvable Matrix Integrals
We generalize the Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce multi-matrix integrals to the integral over eigenvalues, which in turn is a certain tau function. We also consider a generalization of the Kontsevich integral.
متن کاملFinite volume partition functions and Itzykson - Zuber integrals
We find the finite volume QCD partition function for different quark masses. This is a generalization of a result obtained by Leutwyler and Smilga for equal quark masses. Our result is derived in the sector of zero topological charge using a generalization of the Itzykson-Zuber integral appropriate for arbitrary complex matrices. We present a conjecture regarding the result for arbitrary topolo...
متن کاملMicroscopic Spectrum of the QCD Dirac Operator in Three Dimensions
The microscopic spectral correlators of the Dirac operator in three-dimensional Yang-Mills theory coupled to fundamental fermions and with three or more colours are derived from the supersymmetric formulation of partially quenched effective Lagrangians. The flavour supersymmetry breaking patterns are appropriately identified and used to calculate the corresponding finite volume partition functi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005