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TMF, 2010, Volume 162, Number 1, Pages 3–40 (Mi tmf6453)  

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
\by A.~Yu.~Morozov
\paper Unitary integrals and related matrix models
\jour TMF
\yr 2010
\vol 162
\issue 1
\pages 3--40
\jour Theoret. and Math. Phys.
\yr 2010
\vol 162
\issue 1
\pages 1--33

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    This publication is cited in the following articles:
    1. Balantekin A.B., “Character expansions in physics”, Symmetries in Nature, AIP Conf. Proc., 1323, 2010, 1–5  crossref  isi  scopus
    2. Mironov A., Morozov A., Shakirov Sh., “A direct proof of AGT conjecture at beta=1”, J. High Energy Phys., 2011, no. 2, 067  crossref  mathscinet  zmath  isi  elib  scopus
    3. Mironov A., Morozov A., Shakirov Sh., “Brezin-Gross-Witten model as “pure gauge” limit of Selberg integrals”, J. High Energy Phys., 2011, no. 3, 102  crossref  mathscinet  zmath  isi  scopus
    4. Karczmarek J.L., Semenoff G.W., “Large representation recurrences in large $N$ random unitary matrix models”, J. High Energy Phys., 2011, no. 10, 066  crossref  mathscinet  zmath  isi  elib  scopus
    5. Alexandrov A., “Matrix models for random partitions”, Nuclear Phys B, 851:3 (2011), 620–650  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Alexandrov A., Mironov A., Morozov A., Natanzon S., “Integrability of Hurwitz partition functions”, J. Phys. A, 45:4 (2012), 045209, 10 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. 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.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. JETP Letters, 95:11 (2012), 586–593  mathnet  crossref  isi  elib  elib
    10. Romo M., Tierz M., “Unitary Chern–Simons matrix model and the Villain lattice action”, Phys. Rev. D, 86:4 (2012), 045027, 10 pp.  crossref  adsnasa  isi  scopus
    11. 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.  crossref  mathscinet  zmath  isi  scopus
    12. Dubinkin O., “On the Virasoro Constraints For Torus Knots”, J. Phys. A-Math. Theor., 47:48 (2014), 485203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Alexandrov A. Mironov A. Morozov A. Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080  crossref  mathscinet  zmath  isi  scopus
    14. Mironov A., Morozov A., “Correlators in Tensor Models From Character Calculus”, Phys. Lett. B, 774 (2017), 210–216  crossref  isi  scopus
    15. Mironov A. Morozov A., “On Determinant Representation and Integrability of Nekrasov Functions”, Phys. Lett. B, 773 (2017), 34–46  crossref  mathscinet  zmath  isi  scopus
    16. Itoyama H. Mironov A. Morozov A., “Cut and Join Operator Ring in Tensor Models”, Nucl. Phys. B, 932 (2018), 52–118  crossref  mathscinet  zmath  isi  scopus
    17. Mironov A. Morozov A., “Sum Rules For Characters From Character-Preservation Property of Matrix Models”, J. High Energy Phys., 2018, no. 8, 163  crossref  zmath  isi  scopus
    18. Mironov A. Morozov A., “Q-Painleve Equation From Virasoro Constraints”, Phys. Lett. B, 785 (2018), 207–210  crossref  zmath  isi  scopus
    19. Galakhov D., “Why Is Landau-Ginzburg Link Cohomology Equivalent to Khovanov Homology?”, J. High Energy Phys., 2019, no. 5, 085  crossref  isi
    20. Kanazawa T., “Unitary Matrix Integral For Qcd With Real Quarks and the Goe-Gue Crossover”, Phys. Rev. D, 102:3 (2020), 034036  crossref  mathscinet  isi
    21. Anokhina A.S., “Knot Polynomials From Gt-Matrices: Where Is Physics?”, Phys. Part. Nuclei, 51:2 (2020), 172–219  crossref  isi
    22. Betzios P., Papadoulaki O., “Fzzt Branes and Non-Singlets of Matrix Quantum Mechanics”, J. High Energy Phys., 2020, no. 7, 157  crossref  mathscinet  isi
    23. 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  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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