Supersymmetric Gauge Theories on the Five-Sphere

TL;DR

This paper develops supersymmetric gauge theories on a five-sphere, explicitly deriving their transformations and actions, and applies localization to reduce the path integral to instanton and Coulomb moduli integrals.

Contribution

It constructs 5d supersymmetric gauge theories on the five-sphere with explicit SUSY transformations and actions, and applies localization to simplify the path integral.

Findings

Path integral reduces to instanton and Coulomb moduli integrals

Explicit SUSY transformations derived from Noether and supergravity

Framework enables exact computations in 5d supersymmetric theories

Abstract

We construct Euclidean 5d supersymmetric gauge theories on the five-sphere with vector and hypermultiplets. The SUSY transformation and the action are explicitly determined from the standard Noether procedure as well as from off-shell supergravity. Using localization techniques, the path-integral is shown to be restricted to the integration over a generalization of instantons on CP^2 and the Coulomb moduli.