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Exact results for perturbative Chern-Simons theory with complex gauge group
Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom .ORCID iD: 0000-0001-6191-7769
2009 (English)In: Communications in Number Theory and Physics, ISSN 1931-4523, E-ISSN 1931-4531, Vol. 3, no 2, 363-443 p.Article in journal (Refereed) Published
Abstract [en]

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.
National Category
Natural Sciences
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URN: urn:nbn:se:kth:diva-163822ISI: 000283332300004Scopus ID: 2-s2.0-77952552744OAI: oai:DiVA.org:kth-163822DiVA: diva2:802371
Note

QC 20150413

Available from: 2015-04-12 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approved

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Lenells, Jonatan

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