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.
Highlights
Making sense of the fundamental quantum nature of matter within the context of general relativity (GR) [1] is the holy grail of modern theoretical physics
We saw that the procedure to include these extra nonlinear terms does not necessarily force us to look at interaction terms which result in at most second order equations of motion, rather one can have higher order terms present in the theory which can still propagate the required degrees
Ghostly degrees can be removed from the classical picture, they reappear after quantum corrections
Summary
Making sense of the fundamental quantum nature of matter within the context of general relativity (GR) [1] is the holy grail of modern theoretical physics. As opposed to generalized Proca (GP) theories, its decoupling limit (DL) is not restricted to second order equations of motion while still only propagating 3 healthy degrees of freedom and coincides with the DL of ghost-free massive gravity in the scalar-vector sector [36,37,38,39]. IV up to quartic order in the fields and confirm our decoupling limit analysis Both theories have the same quantum implications and the arising counterterms have the same operator structure and the mass scaling
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