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Challenges of β-deformation

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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 β from unity is connected with the “exit from the free-fermion point” in two-dimensional conformal theories, from the symmetric graviphoton field with ∈2 = −∈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.

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  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    A. Yu. Morozov

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 173, No. 1, pp. 104–126, October, 2012.

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Morozov, A.Y. Challenges of β-deformation. Theor Math Phys 173, 1417–1437 (2012). https://doi.org/10.1007/s11232-012-0123-5

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