Quantum stability of Proca-Nuevo

Abstract

The construction of general derivative self-interactions for a massive Proca field relies on the well-known condition for constrained systems of having a degenerate Hessian. The nature of the existing constraints algebra will distinguish among different classes of interactions. Proca-Nuevo interactions enjoy a non-trivial constraint by mixing terms of various order whereas Generalized Proca interactions satisfy the degeneracy condition order by order for each individual Lagrangians. In both cases the vector field propagates at most three degrees of freedom. It has been shown that the scattering amplitudes of Proca-Nuevo arising at the tree level always differ from those of the Generalized Proca, implying their genuinely different nature and a lack of relation by local field redefinitions. In this work, we show the quantum stability of the Proca-Nuevo theory below a specific UV cut-off. Although Proca-Nuevo and Generalized Proca are different inherently in their classical structure, both have the same high energy behaviour when quantum corrections are taken into account. The arising counter terms have the exact same structure and scaling. This might indicate that whatever UV completion they may come from, we expect it to be of similar nature.