Cech, Dolbeault and de Rham cohomologies in Chern-Simons and BF theories

Details Cech, Dolbeault and de Rham cohomologies in Chern-Simons and BF theories Cech, Dolbeault and de Rham cohomologies in Chern-Simons and BF theories

2001-01-23

arxiv.org/abs/hep-th/0101150v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX2e, to appear in proceedings of the XXIII International Colloquium on Group Theoretical Methods in Physics (Jul

Scientific paper

Topological Chern-Simons (CS) and BF theories and their holomorphic analogues are discussed in terms of de Rham and Dolbeault cohomologies. We show that Cech cohomology provides another useful description of the above topological and holomorphic field theories. In particular, all hidden (nonlocal) symmetries of non-Abelian CS and BF theories can be most clearly seen in the Cech approach. We consider multidimensional Manin-Ward integrable systems and describe their connections with holomorphic BF theories. Dressing symmetries of these generic integrable systems are briefly discussed.

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