Unitary Integrals and Related Matrix Models

Details Unitary Integrals and Related Matrix Models Unitary Integrals and Related Matrix Models

2009-06-18

arxiv.org/abs/0906.3518v3

Theor.Math.Phys.162:1-33,2010; Teor.Mat.Fiz.161:3-40,2010

Physics

High Energy Physics

High Energy Physics - Theory

27 pages

Scientific paper

10.1007/s11232-010-0001-y

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. Of technical tools emphasized is the method of character expansions. The subject of unitary integrals remains highly under-investigated and a lot of new results are expected in this field when it attracts sufficient attention.

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