Published December 8, 2015
| Submitted
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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) 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.
Additional Information
We thank A. Lauda and D. Rose for many patient and very helpful explanations, as well as J. Kamnitzer, M. Khovanov, A. Lobb, M. Mackaay, L. Rozansky, M. Stosic, C. Stroppel, C. Teleman, B. Webster, and P. Wedrich for helpful comments and advice. We also thank participants of the "Knot homologies, BPS states, and SUSY gauge theories" program at the Simons Center for Geometry and Physics for useful discussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.Attached Files
Submitted - 1507.06318v1.pdf
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1507.06318v1.pdf
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Additional details
- Eprint ID
- 62645
- Resolver ID
- CaltechAUTHORS:20151207-102030601
- DE-SC0011632
- Department of Energy (DOE)
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2015-12-08Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics