Exact Results for Perturbative ChernSimons Theory with Complex Gauge Group
Abstract
We develop several methods that allow us to compute allloop partition functions in perturbative ChernSimons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a nonabelian 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) ChernSimons theory is an example of such a theory.
 Publication:

arXiv eprints
 Pub Date:
 March 2009
 arXiv:
 arXiv:0903.2472
 Bibcode:
 2009arXiv0903.2472D
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra
 EPrint:
 60 pages, 9 figures