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Surface defects in gauge theory and KZ equation

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arxiv 2103.12611 v3 pith:QPCF675S submitted 2021-03-23 hep-th math.AGmath.QAmath.RT

Nikita Nekrasov , Alexander Tsymbaliuk This is my paper · ORCID
classification hep-thmath.AGmath.QAmath.RT
keywords gaugetheoryconformaldeterminedequationhypermultipletssurfacealgebra
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

  2. (1,k) CFT and RH problem with the c=-2 case

    math-ph 2026-07 conditional novelty 6.0 of 10

    For (1,k) Virasoro models, periodic vertex operators plus two degenerate fields solve a modified Riemann–Hilbert problem; in the k=2, c=-2 case the solution is explicit and satisfies new bilinear identities.

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