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arXiv · 0903.2472

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

Tudor Dimofte·Sergei Gukov·Jonatan Lenells·Don Zagier
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Abstract

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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Tudor Dimofte, Sergei Gukov, Jonatan Lenells, Don Zagier. 2009-03-13. Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group. https://arxiv.org/abs/0903.2472

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