On the consistency of Lorentz-Violating Yang-Mills theories: Gauge invariance and non-perturbative effects

TL;DR

This paper explores the consistency of Lorentz-violating Yang-Mills theories, proposing a gauge-invariant mass term, analyzing foundational aspects, and connecting to non-perturbative effects and Gribov ambiguities in various gauges.

Contribution

It introduces a gauge-invariant mass extension of Lorentz-violating Yang-Mills theories and formulates a BRST-invariant Gribov-Zwanziger action incorporating Lorentz violation.

Findings

The model simplifies in the Landau gauge.

The massive extension serves as an effective tool for infrared analysis.

A BRST-invariant formulation of Gribov-Zwanziger with Lorentz violation is provided.

Abstract

Previous investigations on the renormalizability properties of Lorentz-violating Yang-Mills (LVYM) theories in the Landau gauge have pointed out the necessity of the inclusion of a mass-like term for the gauge fields. If one aims at generalizing the theory to a more complicated gauge, such a mass-like term can bring severe issues regarding gauge-dependence of correlation functions of observables. We propose a Lorentz-violating Yang-Mills theory supplemented by a gauge-invariant mass term which generalizes the model in the Landau gauge. We discuss the foundational aspects of the model and highlight how it simplifies in the Landau gauge. Following the recent literature in pure Yang-Mills theories, we remark how the proposed massive extension of LVYM theories can be used as an effective model to access infrared properties within perturbation theory. Finally, we present a BRST-invariant formulation of the so-called Refined Gribov-Zwanziger action in the presence of Lorentz-violating terms in linear covariant gauges and the underlying tree-level gauge-field propagator which is enriched by the non-perturbative information carried by the elimination of Gribov copies.