Regimes of $3D$ Yang--Mills theory in the presence of a constant vector background

TL;DR

This paper investigates how a constant vector background affects 3D Yang-Mills-Higgs theory, revealing that the aether term influences the transition between nonperturbative and perturbative regimes, with implications for Lorentz symmetry breaking.

Contribution

It demonstrates the emergence of the non-Abelian aether term as a one-loop correction and analyzes its impact on the theory's regime transition in the presence of a constant vector background.

Findings

The aether term arises as a one-loop correction.

The aether coupling constant can drive the theory between regimes.

Lorentz symmetry is broken by the background.

Abstract

In this paper, we take into account the Gribov copies present in 3D Yang-MIlls-Higgs theory with a constant vector background whose presence breaks the Lorentz symmetry. The constant vector background is introduced within the non-Abelian aether term. Here, we show that this term arises as a one-loop correction. The influence of the aether coupling constant on the system is treated afterwards. As a result, we find that for some values of it the theory can be driven from a nonperturbative regime to a perturbative one. In this paper, we work with the Higgs field in the fundamental representation and in the Landau gauge.