Junctions of surface operators and categorification of quantum groups

Chun, Sungbong; Gukov, Sergei; Roggenkamp, Daniel

Junctions of surface operators and categorification of quantum groups

Sungbong Chun
(
- Caltech
)
,
Sergei Gukov
(
- Caltech
)
,
Daniel Roggenkamp
(
- U. Heidelberg, ITP
)

Jul 22, 2015

63 pages

e-Print:

1507.06318 [hep-th]

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Abstract: (arXiv)

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.

Note:

62 pages, 33 figures, minor changes, references added

operator: surface
quantum group
category
Chern-Simons term
Wilson loop
network
SU(N)
foam
matrix: factorization
field theory: topological

References(116)

Figures(44)

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