Chun, Sungbong and Gukov, Sergei and Roggenkamp, Daniel (2015) Junctions of surface operators and categorification of quantum groups. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20151207-102030601
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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.
| Item Type: | Report or Paper (Discussion Paper) | ||||||
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| 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. | ||||||
| Group: | Walter Burke Institute for Theoretical Physics | ||||||
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| DOI: | 10.48550/arXiv.1507.06318 | ||||||
| Record Number: | CaltechAUTHORS:20151207-102030601 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20151207-102030601 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 62645 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 08 Dec 2015 21:49 | ||||||
| Last Modified: | 02 Jun 2023 00:23 |
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