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Perturbative and nonperturbative aspects of complex Chern-Simons Theory

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arxiv 1608.02961 v3 pith:TDN3BQNR submitted 2016-08-09 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords theoryaspectschern-simonscomplexcorrespondenced-3dsomefunctions
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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  1. On geometric bases for A-polynomials II: $\mathfrak{su}_3$ and Kuberberg bracket

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    A new arcade-based planarization technique plus the Kuperberg bracket yields a closed system of classical relations toward su3 A-polynomials, demonstrated on the trefoil.

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