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Perturbative expansion of Chern-Simons theory with non-compact gauge group

1991; Springer Science+Business Media; Volume: 141; Issue: 2 Linguagem: Inglês

10.1007/bf02101513

1432-0916

Dror Bar-Natan, Edward Witten,

Advanced Operator Algebra Research

Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly "unitary" format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified.