The formulation of the Chern-Simons action for general compact Lie groups using Deligne cohomology

Details The formulation of the Chern-Simons action for general compact Lie groups using Deligne cohomology The formulation of the Chern-Simons action for general compact Lie groups using Deligne cohomology

2001-04-23

arxiv.org/abs/hep-th/0104183v1

J. Math. Sci. Univ. Tokyo 8(2001), 223-242.

Physics

High Energy Physics

High Energy Physics - Theory

16 pages

Scientific paper

We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles. If the 3-manifold is closed, the action is a function with values in complex numbers. If the 3-manifold is not closed, then the action is a section of a Hermitian line bundle associated with the Riemann surface which appears as the boundary.

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