Non-perturbative quantum Galileon in the exact renormalization group

TL;DR

This paper studies the non-perturbative renormalization group behavior of the scalar Galileon model, revealing that its symmetry prevents quantum corrections to the couplings, resulting in a trivial fixed point.

Contribution

It introduces multiple expansion schemes for analyzing the Galileon model's renormalization group flow and demonstrates the symmetry's role in maintaining a trivial fixed point.

Findings

Galileon symmetry prevents quantum-induced renormalization of couplings

The model exhibits only a trivial Gaussian fixed point

Different expansion schemes are consistent in analysis

Abstract

We investigate the non-perturbative renormalization group flow of the scalar Galileon model in flat space. We discuss different expansion schemes of the Galileon truncation, including a heat-kernel based derivative expansion, a vertex expansion in momentum space and a curvature expansion in terms of a covariant geometric formulation. We find that the Galileon symmetry prevents a quantum induced renormalization group running of the Galileon couplings. Consequently, the Galileon truncation only features a trivial Gaussian fixed point.