Загадки $\beta$-деформации

Алексей Юрьевич Морозов, Aleksei Yur'evich Morozov
2012 Теоретическая и математическая физика  
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
more » ... rom quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.
doi:10.4213/tmf6967 fatcat:n37h4gnzwbgydeoxseblkum7mm