Perturbative and nonperturbative aspects of complex Chern–Simons theory*This is a contribution to the review issue 'Localization techniques in quantum field theories' (ed Pestun and Zabzine) which contains 17 chapters available at [001]. (13th October 2017)

• Record Type: Journal Article
• Authors: Dimofte, Tudor
• Is Part Of: Journal of physics. Volume 50:Number 44(2017)
• Publication Date: 2017-10-13
• Subjects: Chern–Simons theory -- 3d–3d correspondence -- topological quantum field theory -- supersymmetric localization; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa6a5b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We present an elementary review of some aspects of Chern–Simons theory with complex gauge group S L ( 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.