Twisting to Abelian BF/Chern-Simons Theories

Details Twisting to Abelian BF/Chern-Simons Theories Twisting to Abelian BF/Chern-Simons Theories

1993-08-26

arxiv.org/abs/hep-th/9308127v1

Nucl.Phys. B415 (1994) 353-372

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, CTP #2237, LaTeX

Scientific paper

10.1016/0550-3213(94)90115-5

Starting from a $D=3$, $N=4$ supersymmetric theory for matter fields, a twist with a Grassmann parity change is defined which maps the theory into a gauge fixed, abelian $BF$ theory on curved 3-manifolds. After adding surface terms to this theory, the twist is seen to map the resulting supersymmetric action to two uncoupled copies of the gauge fixed Chern-Simons action. In addition, we give a map which takes the $BF$ and Chern-Simons theories into Donaldson-Witten TQFT's. A similar construction, but with $N=2$ supersymmetry, is given in two dimensions.

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