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 Stückelberg 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.
Highlights
In a cosmological model one might be interested in an axion potential with a very large field range, but at the same time may want a large coupling of the axion to gauge fields
The only necessarily abelian gauge fields that we discuss will be those in section 3 that eat axions to acquire a mass, and the higher-dimensional gauge field in section 4 that is used to engineer a simple scenario with monodromy. (In both cases one could consider nonabelian extensions, but this would complicate the physics without obvious dividends.)
In order to achieve hierarchies between an axion’s coupling to different gauge fields, or between an axion field range and the scale suppressing its coupling to a gauge field, we find the following options:
Summary
Readers who are thoroughly familiar with the reason why aF F couplings are quantized, and how to precisely formulate this condition in theories with fermions, can safely skip this subsection, though it may be useful for establishing our conventions. Because we will be studying scenarios in which axions may not have canonical kinetic terms, it is often useful to consider dimensionless axion fields θ which are normalized to have period 2π, θ(x) ∼= θ(x) + 2πn, n ∈ Z These identifications on field space may be thought of as discrete gauge symmetries. In certain theories, such gauge symmetries may be spontaneously broken, in which case an axion may appear to acquire a non-periodic potential or other interactions that violate the symmetry. The quantization rules (1.3) or (1.7) apply for axion couplings to U(1) gauge fields or to nonabelian gauge fields, up to a change in the linear combination of coefficients appearing in (1.7) that depends on the Dynkin index of the gauge representation of the fermions. The only necessarily abelian gauge fields that we discuss will be those in section 3 that eat axions to acquire a mass, and the higher-dimensional gauge field in section 4 that is used to engineer a simple scenario with monodromy. (In both cases one could consider nonabelian extensions, but this would complicate the physics without obvious dividends.)
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