Axion Periodicity and Coupling Quantization in the Presence of Mixing

TL;DR

This paper investigates how axion mixing affects periodicity and coupling quantization, showing that giving axions a mass can relax constraints and alter effective field ranges, with implications for EFTs and gauge theories.

Contribution

It demonstrates that massless axions inherit UV periodicity constraints, but adding mass relaxes these constraints and modifies effective field ranges, clarifying misconceptions in the literature.

Findings

Massless axions inherit UV periodicity constraints.

Massive axions can relax these constraints and enlarge field ranges.

Eaten axions do not have large effective field ranges, contrary to some claims.

Abstract

Mixing of axion fields is widely used to generate EFTs with phenomenologically advantageous features, such as hierarchies between axion couplings to different gauge fields and/or large effective field ranges. While these features are strongly constrained by periodicity for models with only a single axion, mixing has been used in the literature (sometimes incorrectly) to try to evade some of these constraints. In this paper, we ask whether it is possible to use axion mixing to generate an EFT of axions that evades these constraints by flowing to a theory of a non-compact scalar in the IR. We conclude that as long as the light axion is exactly massless, it will inherit the periodicity and associated constraints of the UV theory. However, by giving the light axion a mass, we can relax these constraints with effects proportional to the axion mass squared, including non-quantized couplings and the realignment of monodromy to a light axion with a larger field range. To show this, we consider various examples of axions mixing with other axions or with non-compact scalar fields, and work in a basis where coupling quantization is manifest. This basis makes it clear that in the case where an axion is eaten through the Higgs or Stuckelberg mechanism, the light axion does not have a large effective field range, in contrast to some recent claims in the literature. Additionally, we relate our results about axion EFTs to a well-known fact about gauge theory: that QFTs with compact gauge groups in the UV flow to QFTs with compact gauge groups in the IR, and make this correspondence precise in the 2+1 dimensional case.