Geometrized quantum Galileons

TL;DR

This paper develops a geometric approach to analyze the quantum corrections of the scalar Galileon model, providing a compact expression for one-loop divergences using heat-kernel techniques and curvature invariants.

Contribution

It introduces a geometric formulation of the Galileon model enabling the calculation of one-loop divergences in a closed form using heat-kernel methods.

Findings

Derived a compact expression for one-loop divergences in terms of curvature invariants.

Resummed divergent contributions of all n-point functions into a single effective action.

Provided insights into the renormalization structure of Galileon theories in flat spacetime.

Abstract

We investigate the renormalization structure of the scalar Galileon model in flat spacetime by calculating the one-loop divergences in a closed geometric form. The geometric formulation is based on the definition of an effective Galileon metric and allows to apply known heat-kernel techniques. The result for the one-loop divergences is compactly expressed in terms of curvature invariants of the effective Galileon metric and corresponds to a resummation of the divergent one-loop contributions of all n-point functions. The divergent part of the one-loop effective action therefore serves as generating functional for arbitrary n-point counterterms. We discuss our result within the Galileon effective field theory and give a brief outlook on extensions to more general Galileon models in curved spacetime.