Exact results for perturbative Chern-Simons theory with complex gauge group
2009 (English)In: Communications in Number Theory and Physics, ISSN 1931-4523, Vol. 3, no 2, 363-443 p.Article in journal (Refereed) Published
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group GC, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative GC invariants turn out to be interesting topological invariants, which are very different from the finite-type (Vassiliev) invariants usually studied in a theory with compact gauge group G and a trivial flat connection. 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 topological quantum field theory" and conjecture (with supporting numerical evidence) that SL(2, C) Chern-Simons theory is an example of such a theory.
Place, publisher, year, edition, pages
2009. Vol. 3, no 2, 363-443 p.
IdentifiersURN: urn:nbn:se:kth:diva-163822ISI: 000283332300004ScopusID: 2-s2.0-77952552744OAI: oai:DiVA.org:kth-163822DiVA: diva2:802371
QC 201504132015-04-122015-04-122015-04-13Bibliographically approved