3d Superconformal Theories from Three-Manifolds

TL;DR

This review explores the deep connections between 3d superconformal gauge theories, complex Chern-Simons theory, and Hitchin moduli spaces, highlighting calculable partition functions and their relations to higher-dimensional correspondences.

Contribution

It synthesizes recent developments linking 3d gauge theories with complex Chern-Simons theory and Hitchin moduli spaces, emphasizing the role of localization and quantization.

Findings

Partition functions computed via localization.

Relations between 3d gauge theories and complex Chern-Simons theory.

Connections to 4d/2d correspondences and Hitchin moduli spaces.

Abstract

This is the 10th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It reviews correspondences between three-dimensional gauge theories and complex Chern-Simons theory on suitable three-manifolds. Such correspondences are in many cases deeply related to the 4d/2d correspondence discussed in this collection. The partition functions of the three-dimensional gauge theories are calculable by means of localisation (as discussed in article no. 9 by K. Hosomichi), and the results are related to the quantum theory obtained by quantisation of Hitchin's moduli spaces.