Surface defects in gauge theory and KZ equation
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.
Cite
@article{arxiv.2103.12611,
title = {Surface defects in gauge theory and KZ equation},
author = {Nikita Nekrasov and Alexander Tsymbaliuk},
journal= {arXiv preprint arXiv:2103.12611},
year = {2022}
}
Comments
v3 41 page, 2 figures; some typos fixed, added additional clarifications of the main calculation