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

TL;DR

This paper explores a four-dimensional Yang-Mills-like model that depends on spacetime's complex structure rather than its metric, demonstrating perturbative confinement through explicit energy calculations with static sources.

Contribution

It introduces a covariant Yang-Mills-like action based on complex structures, providing a novel mechanism for confinement independent of non-Abelian gauge group properties.

Findings

Energy between static sources increases linearly with distance.

Explicit proof of perturbative confinement in the model.

Confinement arises from complex structure dependence, not gauge group non-Abelianity.

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.