A Wilson line realization of quantum groups

Nanna Aamand; Dani Kaufman

doi:10.1007/s11005-023-01756-x

A Wilson line realization of quantum groups

Nanna Aamand, Dani Kaufman^*

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group U_ħ(g) . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

Original language	English
Article number	12
Journal	Letters in Mathematical Physics
Volume	114
Issue number	1
Number of pages	19
ISSN	0377-9017
DOIs	https://doi.org/10.1007/s11005-023-01756-x
Publication status	Published - 2024

Bibliographical note

Funding Information:
The authors were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 772960), and the Copenhagen Centre for Geometry and Topology (DNRF151). Our special thanks goes to Kevin Costello, Nathalie Wahl and Ryszard Nest for helpful suggestions and discussions.

Publisher Copyright:
© 2024, The Author(s).

Keywords

17B37
57K16
Chern–Simons theory
Perturbation theory
Primary: 81T45
Quantum group
Secondary: 81T15
Wilson line

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10.1007/s11005-023-01756-xLicence: CC BY

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Cite this

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abstract = "We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group Uħ(g) . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.",

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AU - Aamand, Nanna

AU - Kaufman, Dani

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N2 - We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group Uħ(g) . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

AB - We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group Uħ(g) . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

KW - 17B37

KW - 57K16

KW - Chern–Simons theory

KW - Perturbation theory

KW - Primary: 81T45

KW - Quantum group

KW - Secondary: 81T15

KW - Wilson line

U2 - 10.1007/s11005-023-01756-x

DO - 10.1007/s11005-023-01756-x

M3 - Journal article

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VL - 114

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

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ER -