Can MAG be a predictive EFT? Radiative stability and ghost resurgence in massive vector models

Abstract The rigorous conditions for obtaining sensible predictions in non (proper) renormalizable quantum field theories were derived a long time ago, most notably in the works of Steven Weinberg. In this paper we explicitly illustrate the challenges met in carrying this program within the affine gravity framework, in particular when attempting to pinpoint viable particle propagation. We explore the one-loop structure of some ghost and tachyon-free vector theories to illustrate the role of structural constraints in their interactions, even in the absence of gauge symmetries. Despite the presence of soft-breaking terms, we show how hopes of casting a vector model within the predictive frame of effective field methods hinges on adopting a gauge-like treatment of their interactions. Our focus here is restricted to negative results and no-go theorems, while a forthcoming companion paper will explore viable examples and constructive scenarios.