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arXiv · 1201.4595

Challenges of beta-deformation

A. Morozov
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Abstract

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.

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A. Morozov. 2012-01-22. Challenges of beta-deformation. https://doi.org/10.4213/tmf6967

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