A. Yu. Morozov, “Unitary integrals and related matrix models”, TMF, 162:1 (2010), 3–40; Theoret. and Math. Phys., 162:1 (2010), 1

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 162, Number 1, Pages 3–40
DOI: https://doi.org/10.4213/tmf6453 (Mi tmf6453)

This article is cited in 40 scientific papers (total in 40 papers)

Unitary integrals and related matrix models

A. Yu. Morozov

Institute for Theoretical and Experimental Physics, Moscow, Russia

Full-text PDF (902 kB) Citations (40)

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DOI: https://doi.org/10.4213/tmf6453

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.

Received: 08.07.2009

English version:
Theoretical and Mathematical Physics, 2010, Volume 162, Issue 1, Pages 1–33
DOI: https://doi.org/10.1007/s11232-010-0001-y

Bibliographic databases:

Language: Russian

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

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This publication is cited in the following 40 articles:

A. Mironov, A. Oreshina, A. Popolitov, “Two $\beta$ -ensemble realization of $\beta$ -deformed WLZZ models”, Eur. Phys. J. C, 84:7 (2024)
A. Morozov, A. Oreshina, “On character expansion and Gaussian regularization of Itzykson-Zuber measure”, Physics Letters B, 857 (2024), 139006
A. Mironov, A. Morozov, A. Popolitov, “Commutative families in DIM algebra, integrable many-body systems and q, t matrix models”, J. High Energ. Phys., 2024:9 (2024)
A. Morozov, N. Tselousov, “3-Schurs from explicit representation of Yangian $\textrm{Y}\left({\hat{\mathfrak{gl}}}_1\right)$ . Levels 1–5”, J. High Energ. Phys., 2023:11 (2023)
A. Mironov, V. Mishnyakov, A. Morozov, A. Popolitov, “Commutative families in W∞, integrable many-body systems and hypergeometric τ-functions”, J. High Energ. Phys., 2023:9 (2023)
A. Mironov, V. Mishnyakov, A. Morozov, A. Popolitov, Wei-Zhong Zhao, “On KP-integrable skew Hurwitz τ-functions and their β-deformations”, Physics Letters B, 839 (2023), 137805
V. Mishnyakov, A. Oreshina, “Superintegrability in $\beta$ -deformed Gaussian Hermitian matrix model from W-operators”, Eur. Phys. J. C, 82:6 (2022)
Adolfo Holguin, Shannon Wang, “Giant gravitons, Harish-Chandra integrals, and BPS states in symplectic and orthogonal $\mathcal{N}$ = 4 SYM”, J. High Energ. Phys., 2022:10 (2022)
Takeshi Oota, “Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories”, Nuclear Physics B, 976 (2022), 115718
David Berenstein, Shannon Wang, “BPS coherent states and localization”, J. High Energ. Phys., 2022:8 (2022)
A. Mironov, A. Morozov, Z. Zakirova, “New insights into superintegrability from unitary matrix models”, Physics Letters B, 831 (2022), 137178
Yang D., Zhou Ch., “On An Extension of the Generalized Bgw Tau-Function”, Lett. Math. Phys., 111:5 (2021), 123
Mironov A. Morozov A., “Superintegrability of Kontsevich Matrix Model”, Eur. Phys. J. C, 81:3 (2021), 270
Anokhina A.S., “Knot Polynomials From R-Matrices: Wherefore This Mathematics?”, Phys. Part. Nuclei, 52:3 (2021), 374–419
Kanazawa T., “Unitary Matrix Integral For Two-Color Qcd and the Gse-Gue Crossover in Random Matrix Theory”, Phys. Lett. B, 819 (2021), 136416
Kanazawa T., “Unitary Matrix Integral For Qcd With Real Quarks and the Goe-Gue Crossover”, Phys. Rev. D, 102:3 (2020), 034036
Anokhina A.S., “Knot Polynomials From Gt-Matrices: Where Is Physics?”, Phys. Part. Nuclei, 51:2 (2020), 172–219
Betzios P., Papadoulaki O., “Fzzt Branes and Non-Singlets of Matrix Quantum Mechanics”, J. High Energy Phys., 2020, no. 7, 157
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
Galakhov D., “Why Is Landau-Ginzburg Link Cohomology Equivalent to Khovanov Homology?”, J. High Energy Phys., 2019, no. 5, 085

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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