Higher dimensional abelian Chern-Simons theories and their link invariants

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 R4l+3 through an unconventional field theoretic computation. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4791677]