Treatments and placebos for the pathologies of effective field theories

TL;DR

This paper critically examines the effectiveness of fixing methods for effective field theories (EFTs) when they break down, showing that such fixes often do not approximate the underlying UV theories well, especially in non-vacuum settling scenarios.

Contribution

The study compares fixed EFTs to their UV counterparts in K-essence and nonlinear Proca theories, highlighting limitations of fixing methods in certain breakdown conditions.

Findings

Fixing does not approximate UV theories well when EFTs lose hyperbolicity and do not settle quickly.

The breakdown of EFT validity cannot be remedied by fixing methods.

Fixing methods are insufficient when EFTs do not rapidly approach vacuum solutions.

Abstract

We demonstrate some shortcomings of "fixing the equations," an increasingly popular remedy for time evolution problems of effective field theories (EFTs). We compare the EFTs and their "fixed" versions to the UV theories from which they can be derived in two cases: K-essence and nonlinear Proca theory. We find that when an EFT breaks down due to loss of hyperbolicity, fixing does not approximate the UV theory well if the UV solution does not quickly settle down to vacuum. We argue that this can be related to the EFT approximation itself becoming invalid, which cannot be rectified by fixing.