Yang-Mills Instantons with Lorentz Violation

TL;DR

This paper investigates how small Lorentz-violating perturbations affect instanton solutions in Euclidean Yang-Mills theory, showing that their topological classification remains unchanged and the action is minimally affected.

Contribution

It demonstrates that Lorentz-violating perturbations do not alter the topological classification or the minimal action of instantons in Yang-Mills theory.

Findings

Topological classification remains unchanged with Lorentz violation

Explicit solutions constructed for gauge-invariant quadratic curvature corrections

Action value is unperturbed to lowest order in Lorentz-violating parameters

Abstract

An analysis is performed of instanton configurations in pure Euclidean Yang-Mills theory containing small Lorentz-violating perturbations that maintain gauge invariance. Conventional topological arguments are used to show that the general classification of instanton solutions involving the topological charge is the same as in the standard case. Explicit solutions are constructed for general gauge invariant corrections to the action that are quadratic in the curvature. The value of the action is found to be unperturbed to lowest order in the Lorentz-violating parameters.