Junctions of surface operators and categorification of quantum groups
High Energy Physics - Theory
2016-06-23 v2 Mathematical Physics
Geometric Topology
math.MP
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.1507.06318,
title = {Junctions of surface operators and categorification of quantum groups},
author = {Sungbong Chun and Sergei Gukov and Daniel Roggenkamp},
journal= {arXiv preprint arXiv:1507.06318},
year = {2016}
}
Comments
62 pages, 33 figures, minor changes, references added