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TMF, 2012, Volume 173, Number 1, Pages 104–126 (Mi tmf6967)  

This article is cited in 12 scientific papers (total in 12 papers)

Challenges of $\beta$-deformation

A. Yu. Morozov


Abstract: We briefly review problems arising in the study of the beta deformation, which turns out to be the most difficult element in a number of modern problems: the deviation of $\beta$ from unity is connected with the "exit from the free-fermion point" in two-dimensional conformal theories, from the symmetric graviphoton field with $\epsilon_2=-\epsilon_1$ in instanton sums in four-dimensional supersymmetric Yang–Mills theories, with the transition from matrix models to beta ensembles, from HOMFLY polynomials to superpolynomials in the Chern–Simons theory, from quantum groups to elliptic and hyperbolic algebras, and so on. We mainly attend to issues related to the Alday–Gaiotto–Tachikawa correspondence and its possible generalizations.

Keywords: matrix model, beta ensemble, conformal theory, Alday–Gaiotto–Tachikawa correspondence, knot invariant, symmetric function

DOI: https://doi.org/10.4213/tmf6967

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English version:
Theoretical and Mathematical Physics, 2012, 173:1, 1417–1437

Bibliographic databases:

Received: 22.02.2012

Citation: A. Yu. Morozov, “Challenges of $\beta$-deformation”, TMF, 173:1 (2012), 104–126; Theoret. and Math. Phys., 173:1 (2012), 1417–1437

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v173/i1/p104

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

    This publication is cited in the following articles:
    1. Piatek M., “Classical Torus Conformal Block, N=2Twisted Superpotential and the Accessory Parameter of Lame Equation”, J. High Energy Phys., 2014, no. 3, 124  crossref  isi  elib
    2. Witte N.S. Forrester P.J., “Moments of the Gaussian Beta Ensembles and the Large-N Expansion of the Densities”, J. Math. Phys., 55:8 (2014), 083302  crossref  mathscinet  zmath  adsnasa  isi
    3. Anokhina A. Morozov A., “Towards R-Matrix Construction of Khovanov-Rozansky Polynomials i. Primary T-Deformation of Homfly”, J. High Energy Phys., 2014, no. 7, 063  crossref  mathscinet  zmath  isi  elib
    4. Morozov A. Smirnov A., “Towards the Proof of AGT Relations With the Help of the Generalized Jack Polynomials”, Lett. Math. Phys., 104:5 (2014), 585–612  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Itoyama H., Yoshioka R., “Developments of Theory of Effective Prepotential From Extended Seiberg-Witten System and Matrix Models”, Prog. Theor. Exp. Phys., 2015, no. 11, 11B103  crossref  mathscinet  zmath  isi
    6. Morozov A., Morozov A., Popolitov A., “on Matrix-Model Approach To Simplified Khovanov-Rozansky Calculus”, Phys. Lett. B, 749 (2015), 309–325  crossref  zmath  adsnasa  isi  elib
    7. Mironov A., Morozov A., Morozov A., Ramadevi P., Singh V.K., “Colored Homfly Polynomials of Knots Presented as Double Fat Diagrams”, J. High Energy Phys., 2015, no. 7, 109  crossref  mathscinet  zmath  isi
    8. Mironov A., Morozov A., Sleptsov A., “Colored Homfly Polynomials For the Pretzel Knots and Links”, J. High Energy Phys., 2015, no. 7, 069  crossref  mathscinet  isi
    9. A. Yu. Morozov, A. A. Morozov, A. V. Popolitov, “Matrix model and dimensions at hypercube vertices”, Theoret. and Math. Phys., 192:1 (2017), 1039–1079  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
    11. Morozov A., “On W-Representations of Beta- and Q, T-Deformed Matrix Models”, Phys. Lett. B, 792 (2019), 205–213  crossref  mathscinet  isi  scopus
    12. Morozov A., “On Exclusive Racah Matrices (S)Over-Bar For Rectangular Representations”, Phys. Lett. B, 793 (2019), 116–125  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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