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

Abstract

Abstract We consider a non-Abelian Lee–Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin 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 β − 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 β − 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 are fixed in these regimes: they are no more the propagating degrees of freedom in the infrared-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit M → ∞ , one recovers the standard results for the local non-Abelian Yang-Mills theory.