Covariant effective action for generalized Proca theories

Abstract

Abstract We investigate the quantum stability of generalised Proca theories in curved spacetime treating gravity as a dynamical field. To compute the quantum gravitational corrections, we evaluate the divergent part of the effective action at one-loop level using Vilkovisky-DeWitt formalism, 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.