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Exact results for perturbative Chern-Simons theory with complex gauge group
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Dimofte, T. (author)
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Gukov, S. (author)
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- Lenells, Jonatan, 1981- (author)
- Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Zagier, D. (author)
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(creator_code:org_t)
- International Press of Boston, 2009
- 2009
- English.
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In: Communications in Number Theory and Physics. - : International Press of Boston. - 1931-4523 .- 1931-4531. ; 3:2, s. 363-443
- Related links:
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http://www.intlpress...
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https://urn.kb.se/re...
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https://doi.org/10.4...
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Abstract
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- 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.
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