2016/08/31 by Tudor Dimofte
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa6a5b
This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf
arxiv created 2016/10/15 · arxiv updated 2017/10/25
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.