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This article is cited in 23 scientific papers (total in 23 papers)
Unitary integrals and related matrix models
A. Yu. Morozov
Institute for Theoretical and Experimental Physics, Moscow,
Russia
Abstract:
We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties: the ordinary unitary, the Brezin–Gross–Witten, and the Harish-Chandra–Itzykson–Zuber models. We especially emphasize the nontrivial aspects of the theory, from the De Wit–t'Hooft anomaly in unitary integrals to the problem of calculating correlators with the Itzykson–Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still insufficiently investigated, and many new results should be expected as this field attracts increased attention.
Keywords:
matrix model, unitary group
DOI:
https://doi.org/10.4213/tmf6453
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English version:
Theoretical and Mathematical Physics, 2010, 162:1, 1–33
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Received: 08.07.2009
Citation:
A. Yu. Morozov, “Unitary integrals and related matrix models”, TMF, 162:1 (2010), 3–40; Theoret. and Math. Phys., 162:1 (2010), 1–33
Citation in format AMSBIB
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Karczmarek J.L., Semenoff G.W., “Large representation recurrences in large $N$ random unitary matrix models”, J. High Energy Phys., 2011, no. 10, 066
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Alexandrov A., “Matrix models for random partitions”, Nuclear Phys B, 851:3 (2011), 620–650
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Alexandrov A., Mironov A., Morozov A., Natanzon S., “Integrability of Hurwitz partition functions”, J. Phys. A, 45:4 (2012), 045209, 10 pp.
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Mironov A., Morozov A., Shakirov Sh., “Towards a proof of AGT conjecture by methods of matrix models”, Internat. J. Modern Phys. A, 27:1 (2012), 1230001, 32 pp.
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Mironov A., Morozov A., Shakirov Sh., Smirnov A., “Proving AGT conjecture as HS duality: Extension to five dimensions”, Nuclear Phys. B, 855:1 (2012), 128–151
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JETP Letters, 95:11 (2012), 586–593
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Romo M., Tierz M., “Unitary Chern–Simons matrix model and the Villain lattice action”, Phys. Rev. D, 86:4 (2012), 045027, 10 pp.
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Mironov A. Morozov A. Morozov And., “Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid”, J. High Energy Phys., 2012, no. 3, 034, 33 pp.
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Alexandrov A. Mironov A. Morozov A. Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080
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Kanazawa T., “Unitary Matrix Integral For Qcd With Real Quarks and the Goe-Gue Crossover”, Phys. Rev. D, 102:3 (2020), 034036
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Anokhina A.S., “Knot Polynomials From Gt-Matrices: Where Is Physics?”, Phys. Part. Nuclei, 51:2 (2020), 172–219
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Andreev A. Popolitov A. Sleptsov A. Zhabin A., “Genus Expansion of Matrix Models and ? Expansion of Kp Hierarchy”, J. High Energy Phys., 2020, no. 12, 38
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