Perturbative reduction of derivative order in EFT

TL;DR

This paper discusses how higher derivative corrections in effective field theories can be systematically removed or reinterpreted to avoid introducing extra degrees of freedom, using field redefinitions and focusing on Horndeski theories.

Contribution

It demonstrates that higher derivative corrections can be eliminated via field redefinitions, simplifying EFTs and aligning them with Horndeski theories, and advocates restricting EFT expansions to avoid extra degrees of freedom.

Findings

Field redefinitions effectively remove higher derivative corrections.

Effects of first-order corrections are captured by Horndeski theories.

Restricting EFTs to terms without extra degrees of freedom is advisable.

Abstract

Higher derivative corrections are ubiquitous in effective field theories, which seemingly introduces new degrees of freedom at successive order. This is actually an artefact of the implicit local derivative expansion defining effective field theories. We argue that higher derivative corrections that introduce additional degrees of freedom should be removed and their effects captured either by lower derivative corrections, or special combinations of higher derivative corrections not propagating extra derees of freedom. Three methods adapted for this task are examined and field redefinitions are found to be most appropriate. First order higher derivative corrections in a scalar tensor theory are removed by field redefinition and it is found that their effects are captured by a subset of Horndeski theories. A case is made for restricting the effective field theory expansions in principle to only terms not introducing additional degrees of freedom.