Einstein-Yang-Mills Theory: Gauge Invariant Charges and Linearization Instability

TL;DR

This paper extends gauge-invariant charge definitions to Einstein-Yang-Mills theory with cosmological backgrounds and analyzes conditions under which linear perturbation theory remains valid.

Contribution

It introduces gauge-invariant electric and magnetic charges in curved spacetime and investigates linearization stability conditions in Einstein-Yang-Mills theory.

Findings

Gauge-invariant charges include gravity contributions for non-zero background fields.

Conditions for linearization instability are established.

Perturbation theory validity depends on specific background and gauge configurations.

Abstract

We construct the gauge-invariant electric and magnetic charges in Yang-Mills theory coupled to cosmological General Relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser. For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.