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

Dimofte, Tudor and Gukov, Sergei and Lenells, Jonatan and Zagier, Don (2009) Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group. Communications in Number Theory and Physics, 3 (2). pp. 363-443. ISSN 1931-4523. https://resolver.caltech.edu/CaltechAUTHORS:20100202-111957900

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/0903.2472arXivDiscussion Paper
http://dx.doi.org/10.4310/CNTP.2009.v3.n2.a4DOIArticle
http://intlpress.com/site/pub/pages/journals/items/cntp/content/vols/0003/0002/a004/index.htmlPublisherArticle
Additional Information:© 2009 International Press. Received March 18, 2009. We would like to thank D. Auroux, N. Dunfield, S. Garoufalidis, K. Hikami, T. Mrowka, W. Neumann, E. Witten, and C. Zickert for useful discussions and correspondence. Research of SG is supported in part by NSF Grant PHY-0757647 and in part by the Alfred P. Sloan Foundation. JL acknowledges support from a Marie Curie Intra-European Fellowship. TD acknowledges support from a National Defense Science and Engineering Graduate Fellowship. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Funders:
Funding AgencyGrant Number
NSFPHY-0757647
Alfred P. Sloan FoundationUNSPECIFIED
Marie Curie FellowshipUNSPECIFIED
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20100202-111957900
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100202-111957900
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17372
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:10 Feb 2010 23:26
Last Modified:03 Oct 2019 01:27

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