Asymptotic Safety in Generalized Proca Theories

TL;DR

This paper explores the potential for ultraviolet completion of Generalized Proca Theories through asymptotic safety, identifying a specific fixed point that could serve as a consistent quantum foundation for these dark energy models.

Contribution

It demonstrates the existence of a non-Gaussian ultraviolet fixed point in Generalized Proca Theories, highlighting a candidate for their fundamental quantum completion.

Findings

Identified a Proca fixed point with a non-tachyonic mass.

Found multiple fixed points close to each other.

Compared features with the Reuter fixed point in quantum gravity.

Abstract

Generalized Proca Theories are the most general higher-derivative extensions of a massive vector field that retain second-order equations of motion. They are phenomenologically interesting as models of dynamical dark energy that, unlike scalar-tensor theories, can naturally accommodate cosmological anisotropies. A key open question is whether such theories can be fundamental. As a first step in this direction, we investigate whether they admit an ultraviolet completion within a quantum field theory framework, working with a truncation comprising up to four powers of the Proca field and up to two derivatives. We find a triplet of non-Gaussian ultraviolet fixed points, that lie very close to one another. Only one of them features a non-tachyonic Proca mass and could thus serve as a consistent ultraviolet completion for Generalized Proca Theories. We name it the Proca fixed point. We discuss its stability and contrast its features with those of the standard Reuter fixed point of the asymptotic safety scenario for quantum gravity and matter. In particular, we show that the Gaussian and Reuter fixed points lie on singular hypersurfaces of the flow of Generalized Proca Theories, yet can act as quasi-fixed points in certain regimes.