Gauge Theories on de Sitter space and Killing Vectors

TL;DR

This paper develops a covariant formulation of p-form gauge theories on de Sitter space by stereographic projection from Minkowski space, enabling analysis of anomalies and dualities with a clear geometric approach.

Contribution

It introduces a method using conformal Killing vectors to map gauge theories from Minkowski to de Sitter space, simplifying analysis and revealing new insights.

Findings

Computed the axial anomaly on de Sitter space.

Demonstrated electric-magnetic duality in this framework.

Showed zero curvature limit recovers Minkowski results.

Abstract

We provide a general method for studying a manifestly covariant formulation of $p$-form gauge theories on the de Sitter space. This is done by stereographically projecting the corresponding theories, defined on flat Minkowski space, onto the surface of a de Sitter hyperboloid. The gauge fields in the two descriptions are mapped by conformal Killing vectors allowing for a very transparent analysis and compact presentation of results. As applications, the axial anomaly is computed and the electric-magnetic duality is exhibited. Finally, the zero curvature limit is shown to yield consistent results.