Localization on three-dimensional manifolds

TL;DR

This review discusses the methods of localizing three-dimensional N=2 supersymmetric theories on various compact manifolds, enabling exact calculations of partition functions and observables with applications in theoretical physics.

Contribution

It provides a comprehensive overview of how to formulate supersymmetric actions and perform localization on diverse 3D manifolds, advancing computational techniques in supersymmetric quantum field theories.

Findings

Explicit formulas for partition functions on S^3_b and S^3_b/Z_p

Methodology for constructing supersymmetric actions on curved spaces

Survey of applications in theoretical physics

Abstract

In this review article we describe the localization of three dimensional N=2 supersymmetric theories on compact manifolds, including the squashed sphere, S^3_b, the lens space, S^3_b/Z_p, and S^2 x S^1. We describe how to write supersymmetric actions on these spaces, and then compute the partition functions and other supersymmetric observables by employing the localization argument. We briefly survey some applications of these computations.