Gauge Theories on Sphere and Killing Vectors

TL;DR

This paper develops a covariant formulation of p-form gauge theories on spheres using stereographic projection, employing conformal Killing vectors and spinors to relate flat space and spherical descriptions.

Contribution

It introduces a general method for formulating gauge theories on spheres via stereographic projection, utilizing conformal Killing vectors and spinors for a transparent analysis.

Findings

Reproduces known results for vector gauge theories.

Provides explicit expressions for Killing vectors and spinors.

Establishes a covariant framework for p-form gauge theories on spheres.

Abstract

We provide a general method for studying manifestly $O(n+1)$ covariant formulation of $p$-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge fields in the two descriptions are mapped by conformal Killing vectors while conformal Killing spinors are necessary for the matter fields, allowing for a very transparent analysis and compact presentation of results. General expressions for these Killing vectors and spinors are given. The familiar results for a vector gauge theory are reproduced.