Quantum stability of generalized Proca theories

Abstract

We establish radiative stability of generalized Proca effective field theories. While standard power-counting arguments would conclude otherwise, we find non-trivial cancellations of leading order corrections by explicit computation of divergent one-loop diagrams up to four-point. These results are crosschecked against an effective action based generalized Schwinger–DeWitt method. Further, the cancellations are understood as coming from the specific structure of the theory through a decoupling limit analysis which at the same time allows for an extension of the results to higher orders.

Covariant Effective Action for Generalized Proca Theories

“…As one expects there are no terms in the above expression which blow up in the limit α → 0. The functions f i , gi and g i depend only upon the constant parameters of the theory and are given in Appendix C. We note the following features which we find to be somewhat in agreement with [29] even under inclusion of gravitational corrections.…”

“…The fourth term is the only surviving classical non-linear term in decoupling limit (66) with the last two terms arising from quantum loops. To get a concise picture of how classical non-linearities and quantum induced terms compare with the kinetic terms it is helpful to establish an hierarchy by identifying the classical and quantum expansion parameters[ [29,47,48]]. The quantum corrected action (71) can be written succinctly (by suppressing index notation) as…”

“…can be the only next sensible question to ask. Although a thorough analysis to answer the above question had already been undertaken earlier at one loop level(see [29]), it was limited to generalised proca theory in flat spacetime. In this work we attempt to answer this question for generalised proca theory in curved spacetime treating gravity as a dynamical field.…”

Cosmology of Extended Proca-Nuevo

“…Similarly to their scalar-tensor counterparts, generalized vector-tensor theories have been shown to exhibit intriguing phenomenological properties in astrophysical systems [1][2][3][4][5][6][7] and cosmology [8][9][10][11][12][13][14][15][16][17]. In the latter case, of particular interest, is the fact that a time-dependent vector condensate could behave as a dark energy fluid, driving the observed accelerated cosmic expansion in the present-day universe, with a technically natural vector mass and dark energy scale [18,19].…”

Quantum stability of Proca-Nuevo

“…Soon it was realized, that there exists a finite set of higher order scalar interactions with the same properties, the Galileons [19], leading to a rediscovery of the covariant Horndeski theory [20] as well as a formulation of a vector counter part known as Generalized Proca (GP) [21][22][23] with various cosmological applications on their own right. A crucial aspect of effective field theories (EFT) of this type is their radiadive stability in regimes where the classical irrelevant interactions dominate such that the theory remains viable on scales relevant for the Vainshtein screening, in other words that there exists a regime for which classical non-linearities dominate, while quantum effects are still under control [8,9,[24][25][26][27][28][29][30][31][32][33][34].…”