Aspects of Galileon Non-Renormalization

TL;DR

The paper establishes a robust non-renormalization framework for derivatively coupled EFTs, with a sharp focus on galileons. Through both a diagrammatic background-field proof and general power-counting arguments, it shows that galileon operators are protected from renormalization by galileon loops and, crucially, by loops of heavy fields that couple in a galileon-invariant way. By contrast, gravity, $P(X)$ theories, and the conformal dilaton do not share this protection when heavy fields are integrated out; their leading operators can and do renormalize, with specific beta functions computed for gravity and DBI-like sectors. The results illuminate the peculiar ultraviolet behavior and naturalness of galileon EFTs, with implications for cosmology and IR modifications of gravity, and highlight how symmetry-preserving couplings to heavy physics can shield low-energy galileon structure from quantum corrections.

Abstract

We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and $P(X)$ theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. However, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.

Figures (1)

• Figure 1: The various $2\to 2$ diagrams built solely from galileon operators \ref{['GalileonTerms']}, up to one loop, and their scaling with external momenta. It is clear that the loop diagrams contribute at higher orders in momenta than the tree amplitude.