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arXiv · 1207.1270

Higher dimensional abelian Chern-Simons theories and their link invariants

L. Gallot·E. Pilon·F. Thuillier
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Abstract

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.

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L. Gallot, E. Pilon, F. Thuillier. 2012-07-05. Higher dimensional abelian Chern-Simons theories and their link invariants. https://doi.org/10.1063/1.4791677

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