Higher dimensional abelian Chern-Simons theories and their link invariants

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.

40 pages

References in corpus (1)

• Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space

Cited by in corpus (6)

• Path-integral invariants in abelian Chern-Simons theory
• Abelian BF theory and Turaev-Viro invariant
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• Topological gauge fixing II: a homotopy formulation
• Geometric aspects of interpolating gauge fixing in Chern-Simons Theory
• 3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables