Chern–Simons theory and the R-matrix

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  • Nanna Havn Aamand

It has been a long-standing problem how to relate Chern–Simons theory to the quantum groups. In this paper we recover the classical r-matrix directly from a three-dimensional Chern–Simons theory with boundary conditions, thus creating a direct link to the quantum groups. It is known that the Jones polynomials can be constructed using an R-matrix. We show how these constructions can be seen to arise directly from 3-dimensional Chern–Simons theory.

Original languageEnglish
Article number146
JournalLetters in Mathematical Physics
Volume111
Issue number6
ISSN0377-9017
DOIs
Publication statusPublished - 2021

Bibliographical note

Funding Information:
I would like to thank my supervisor Kevin Costello for helpful guidance. I also wish to thank Victor Py for useful comments along the way. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development, and by the Province of Ontario through the Ministry of Research and Innovation.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

    Research areas

  • Chern-Simons theory, Knot invariants, R-matrices

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