# Junctions of surface operators and categorification of quantum groups

@article{Chun2015JunctionsOS, title={Junctions of surface operators and categorification of quantum groups}, author={Sungbong Chun and Sergei Gukov and Daniel Roggenkamp}, journal={arXiv: High Energy Physics - Theory}, year={2015} }

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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