Gauge Theories on A(dS) space and Killing Vectors

TL;DR

This paper develops a covariant framework for non-abelian gauge theories on A(dS) spaces by stereographic projection from Minkowski space, analyzing gauge fixing, anomalies, and duality.

Contribution

It introduces a unified method to analyze gauge theories on A(dS) spaces using conformal mappings from flat space, including anomaly calculations and duality demonstrations.

Findings

Derived gauge and matter field mappings via conformal Killing vectors and spinors.

Established equivalence of different gauge fixing conditions.

Calculated U(1) axial and non-abelian chiral anomalies on A(dS) space.

Abstract

We provide a general technique for collectively analysing a manifestly covariant formulation of non-abelian gauge theories on both anti de Sitter as well as de Sitter spaces. This is done by stereographically projecting the corresponding theories, defined on a flat Minkowski space, onto the surface of the A(dS) hyperboloid. The gauge and matter fields in the two descriptions are mapped by conformal Killing vectors and conformal Killing spinors, respectively. A bilinear map connecting the spinors with the vector is established. Different forms of gauge fixing conditions and their equivalence are discussed. The U(1) axial anomaly as well as the non-abelian covariant and consistent chiral anomalies on A(dS) space are obtained. Electric-magnetic duality is demonstrated. The zero curvature limit is shown to yield consistent findings.