Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings

TL;DR

This paper explores a non-Abelian Lee-Wick gauge theory, analyzing its BRST invariance, confinement conditions, and non-perturbative beta functions, revealing how heavy ghost states become non-propagating in the IR and connecting to standard Yang-Mills results.

Contribution

It provides the first non-perturbative analysis of Lee-Wick gauge theories, including exact solutions and confinement criteria, extending understanding of strong coupling regimes.

Findings

Beta functions similar to Yang-Mills theory with natural cut-off from Lee-Wick mass scale

Ghosts become non-propagating in the infrared limit

Confinement driven by non-Abelian interactions, recovering standard results as M→∞

Abstract

We consider a non-Abelian Lee--Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin (BRST) invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo-Ojima approach, and obtain the $\beta-$functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar $\beta-$function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee-Wick heavy mass scales (M). We show that the fate of the ghosts is fixed in these regimes: they are no more the propagating degrees of freedom in the infrared (IR)-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit $M\rightarrow\infty $, one recovers the standard results for the local non-Abelian Yang-Mills theory.