TY - JOUR

T1 - Chern–Simons theory and the R-matrix

AU - Aamand, Nanna Havn

N1 - 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.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Chern-Simons theory

KW - Knot invariants

KW - R-matrices

U2 - 10.1007/s11005-021-01485-z

DO - 10.1007/s11005-021-01485-z

M3 - Journal article

AN - SCOPUS:85120729095

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 6

M1 - 146

ER -