Surface defects in gauge theory and KZ equation
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Publication:6363530
DOI10.1007/S11005-022-01511-8arXiv2103.12611MaRDI QIDQ6363530
Nikita Nekrasov, Aleksander Tsymbaliuk
Publication date: 23 March 2021
Abstract: We study the regular surface defect in the Omega-deformed four-dimensional supersymmetric gauge theory with gauge group SU(N) with 2N hypermultiplets in fundamental representation. We prove its vacuum expectation value obeys the Knizhnik-Zamolodchikov equation for the 4-point conformal block of current algebra of a two-dimensional conformal field theory. The level and the vertex operators are determined by the parameters of the Omega-background and the masses of the hypermultiplets; the cross-ratio of the 4 points is determined by the complexified gauge coupling. We clarify that in a somewhat subtle way the branching rule is parametrized by the Coulomb moduli. This is an example of the BPS/CFT relation.
Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Yang-Mills and other gauge theories in quantum field theory (81T13) Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) (81T35)
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