Gauge Field Theory in the Infrared Regime

TL;DR

This paper introduces a Lorentz invariance violation approach to study low-energy gauge theories, linking them to three-dimensional QCD with a Chern-Simons term and an infrared scale-dependent fermion mass.

Contribution

It proposes a novel method of analyzing infrared gauge theories by deforming Poisson brackets, connecting four-dimensional gauge theories to three-dimensional QCD.

Findings

Low-energy gauge theories can be modeled with Lorentz violation.

The deformed theory is equivalent to a gauge theory with a Chern-Simons term.

Fermion mass in 3D QCD relates to the infrared scale.

Abstract

We propose that the low energy behavior of a pure gauge theory can be studied by simply assuming violation of Lorentz invariance which is implemented through a deformation of the canonical Poisson brackets of the theory depending on an infrared scale. The resulting theory is equivalent to a pure gauge theory with a Chern-Simons like term. It is shown that at low energies this theory can be identified with three dimensional QCD where the mass of the fermion is related to the infrared scale.