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Junctions of surface operators and categorification of quantum groups

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arxiv 1507.06318 v2 pith:3FI3XP2D submitted 2015-07-22 hep-th math-phmath.GTmath.MPmath.QA

Sungbong Chun , Sergei Gukov , Daniel Roggenkamp This is my paper · ORCID
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keywords groupsoperatorsquantumsurfacejunctionstheoryarbitrarycategorical
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We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.

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  1. On geometric bases for A-polynomials II: $\mathfrak{su}_3$ and Kuberberg bracket

    hep-th 2025-05 conditional novelty 6.0 of 10

    A new arcade-based planarization technique plus the Kuperberg bracket yields a closed system of classical relations toward su3 A-polynomials, demonstrated on the trefoil.

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