Higher dimensional abelian Chern-Simons theories and their link invariants

摘要

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 R~(4l+3) through an unconventional field theoretic computation.