Gauge and matter superfield theories on $S^2$

TL;DR

This paper formulates gauge and matter superfield theories on a two-dimensional sphere with extended supersymmetry, deriving explicit supergeometry and applying localization techniques to compute partition functions.

Contribution

It introduces a supercoset-based superfield formulation on $S^2$ with explicit supervielbein and derivatives, enabling direct superspace localization calculations.

Findings

Explicit supervielbein and covariant derivatives on $S^2$ supercoset

Superfield actions for gauge and matter multiplets constructed

One-loop partition functions computed using superspace localization

Abstract

We develop a superfield formulation of gauge and matter field theories on a two-dimensional sphere with rigid N=(2,2) as well as extended supersymmetry. The construction is based on a supercoset SU(2|1)/[U(1) x U(1)] containing $S^2$ as the bosonic subspace. We derive an explicit form of supervielbein and covariant derivatives on this coset, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace.