Junctions of surface operators and categorification of quantum groups
Abstract
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) ChernSimons 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.06318
 Bibcode:
 2015arXiv150706318C
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra
 EPrint:
 62 pages, 33 figures, minor changes, references added