Quantum Corrections in Galileons from Matter Loops

TL;DR

This paper investigates how matter loops affect Galileon scalar field theories, revealing that quantum corrections generate higher derivative interactions but remain suppressed and harmless within the effective field theory regime.

Contribution

It provides the first detailed calculation of one-loop matter corrections to Galileon interactions for various covariant couplings, showing their effects and suppression scales.

Findings

Matter loops renormalize Galileon interactions.

Higher order ghost interactions are generated.

Corrections are suppressed by the classical coupling scale.

Abstract

Galileon interactions represent a class of effective field theories that have received much attention since their inception. They can be treated in their own right as scalar field theories with a specific global shift and Galilean symmetry or as a descendant of a more fundamental theory like massive gravity. It is well known that the Galileon theories are stable under quantum corrections thanks to the non-renormalization theorem which is not due to the symmetry. We consider different covariant couplings of this Galileon scalar field with the matter field: the conformal coupling, the disformal coupling and the longitudinal coupling. We compute the one-loop quantum corrections to the Galileon interactions from the coupling to the external matter fields. In all the considered cases of covariant couplings we show that the terms generated by one-loop matter corrections not only renormalize the Galileon interactions but also give rise to higher order derivative ghost interactions. However, the renormalized version of the Galileon interactions as well as the new interactions come at a scale suppressed by the original classical coupling scale and hence are harmless within the regime of validity of the effective field theory.