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Junctions of surface operators and categorification of quantum groups

Chun, Sungbong and Gukov, Sergei and Roggenkamp, Daniel (2015) Junctions of surface operators and categorification of quantum groups. . (Submitted)

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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)
Related URLs:
URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
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
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20151207-102030601
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62645
Deposited By: Tony Diaz
Deposited On:08 Dec 2015 21:49
Last Modified:02 Jun 2023 00:23

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