Covariant Effective Action for Generalized Proca Theories

TL;DR

This paper analyzes the quantum stability of generalized Proca theories in curved spacetime, showing quantum corrections are suppressed under certain conditions, thus supporting the classical Vainshtein mechanism.

Contribution

It introduces a gauge-invariant one-loop effective action calculation for generalized Proca theories using Vilkovisky-DeWitt formalism in curved spacetime.

Findings

Quantum corrections are suppressed by a high UV cutoff.

Quantum corrections remain small even where classical non-linearities dominate.

Supports the viability of the Vainshtein mechanism at quantum level.

Abstract

We investigate quantum stability of the generalised Proca theories in curved spacetime treating gravity as a dynamical field. To compute the quantum gravitational corrections we evaluate divergent part of the effective action at one loop level. We employ Vilkovisky-DeWitt formalism for this task which gives us a gauge invariant and gauge condition independent effective action. It is shown that the quantum corrections are suppressed by a UV cutoff parametrically higher than the Proca mass if the coupling constants are restricted to lie in a certain range. Furthermore it is shown that the quantum corrections remain suppressed even at scales where classical non-linearities dominate over kinetic terms allowing Vainshtein mechanism to work.