2019/08/31 by Cyril Closset, Heeyeon Kim · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1142/s0217751x19300114
published as International Journal of Modern Physics A, Vol. 34, No. 23 (2019) 1930011 · 96 pages. Review for IJMPA. Comments welcome. v2: added references
arxiv created 2019/09/02 · arxiv updated 2019/09/04
We give a pedagogical introduction to the study of supersymmetric partition functions of 3D N=2 supersymmetric Chern-Simons-matter theories (with an R-symmetry) on half-BPS closed three-manifolds---including S3, S2 × S1, and any Seifert three-manifold. Three-dimensional gauge theories can flow to non-trivial fixed points in the infrared. In the presence of 3D N=2 supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.