Perturbative and nonperturbative aspects of complex Chern–Simons theory

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We present an elementary review of some aspects of Chern-Simons theory with complex gauge group SL(N,C). We discuss some of the challenges in defining the theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d correspondence. The 3d-3d correspondence relates partition functions (and other aspects) of complex Chern-Simons theory on a 3-manifold M to supersymmetric partition functions (and other observables) in an associated 3d theory T[M]. Many of these observables may be computed by supersymmetric localization. We present several prominent applications to 3-manifold topology and number theory in light of the 3d-3d correspondence.
Original languageEnglish
Article number443009
Number of pages33
JournalJournal of Physics A: Mathematical and Theoretical
Issue number44
Early online date13 Oct 2017
Publication statusPublished - 3 Nov 2017


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