Perturbative Confinement in a 4-d Lorentzian Complex Structure Dependent YM-like Model

Abstract: I continue the study of a renormalizable four-dimensional generally covariant Yang-Mills-like action, which depends on the Lorentzian complex structure of spacetime and not its metric. The field equations and their integrability conditions are written down explicitly. The model is studied with the presence of two static external sources in the trivial cylindrical complex structure. The energy of two static "colored" sources is found to increase linearly with respect to their distance, providing an explicit proof of their perturbative confinement. In the present model, confinement is not a concequence of the non-Abelian character of the gauge group, but it is implied by the complex structure dependence of the model.