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arXiv · 2103.12611

Surface defects in gauge theory and KZ equation

Nikita Nekrasov·Alexander Tsymbaliuk
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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.

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Nikita Nekrasov, Alexander Tsymbaliuk. 2021-03-23. Surface defects in gauge theory and KZ equation. https://doi.org/10.1007/s11005-022-01511-8

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