Quantum corrections in classicalon theories

Abstract

We use the heat kernel in order to compute the one-loop effective action on a classicalon background. We find that the UV divergences are suppressed relative to the predictions of standard perturbation theory in the interior of the classicalon. There is a strong analogy with the suppression of quantum fluctuations in Galileon theories, within the regions where the Vainshtein mechanism operates (discussed in arXiv:1401.2775). Both classicalon and Galileon theories display reduced UV sensitivity on certain backgrounds. (N. Brouzakis). 1 An interesting possibility is that the absence of a real classical solution in the scattering problem may indicate the presence of a tunnelling solution in the quantum theory [6], so that classicalization is a quantum process.

Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars

“…Our discussion builds on other attempts to investigate quantum corrections in similar theories: in particular, loop corrections to higherderivative scalar theories have been discussed in [68][69][70], with the exact renormalization group employed in [67,72] 6 . The suppression of quantum fluctuations in a similar context has been highlighted in [67,76], as well as in [71,75], the latter from the perspective of classicalisation [41]. Galileon non-renormalisation theorems, including the extensions to heavy loops, have been proven in [77,78] and will be perfectly consistent with our analysis.…”

“…Writing Λ = Λ * where Λ * is some fixed finite scale and is small, we can absorb the powers of into a redefinition of and understand the Λ → 0 limit as a classical scale-invariant limit. This is entirely consistent with the Wilsonian perspective on classicalisation [41] advocated in [42] (see also discussion in [98]) for which the lack of running could have been regarded as a smoking gun [71,75]. Of course, UV completion through classicalisation is only possible if there exist static self-sourcing classicalon profiles whose radius grows with energy.…”

“…For a scalar field exhibiting Vainshtein screening the classicalon corresponds to a macroscopic classical solution to the low-energy field equations. Our analysis in the next section reveals a suppression of quantum fluctuations for strongly-coupled backgrounds, consistent with expectations from classicalisation [71,73]. However, this does not mean that UV completion by classicalisation is necessarily compatible with our Universe, at least for theories that exhibit large-scale Vainshtein screening.…”