Geodesic
Challenges of $\beta$-deformation
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 1, pp. 104-126

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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, conformal theory, Alday–Gaiotto–Tachikawa correspondence, knot invariant, symmetric function.
Mots-clés : beta ensemble 
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     author = {A. Yu. Morozov},
     title = {Challenges of $\beta$-deformation},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_1_a5/}
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A. Yu. Morozov. Challenges of $\beta$-deformation. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 1, pp. 104-126. http://geodesic.mathdoc.fr/item/TMF_2012_173_1_a5/