Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group

Details Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group

2009-03-13

arxiv.org/abs/0903.2472v1

Commun.Num.Theor.Phys.3:363-443,2009

Physics

High Energy Physics

High Energy Physics - Theory

60 pages, 9 figures

Scientific paper

We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, which are very different from finite type (Vassiliev) invariants obtained in a theory with compact gauge group G. We explore various aspects of these invariants and present an example where we compute them explicitly to high loop order. We also introduce a notion of "arithmetic TQFT" and conjecture (with supporting numerical evidence) that SL(2,C) Chern-Simons theory is an example of such a theory.

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