High-Quality Axions from Higher-Form Symmetries in Extra Dimensions

TL;DR

This paper explores how higher-dimensional gauge theories with generalized symmetries can produce high-quality axions that address the strong CP problem, offering new insights into symmetry protection and potential generation mechanisms.

Contribution

It systematically characterizes the role of electric one-form symmetries in protecting axion potentials in extra dimensions and identifies novel ways to break these symmetries to generate axion potentials.

Findings

Electric one-form symmetry protects axion potential in 5D gauge theories.

Breaking the symmetry via matter, gauging, or anomalies generates axion potentials.

New mechanisms involving magnetic monopoles are identified for potential generation.

Abstract

The extra-dimensional axion solves the strong CP problem while largely circumventing the quality problem that plagues its four-dimensional counterparts. Such high quality can be clearly understood in terms of the generalized global symmetries of the higher-dimensional theory. We emphasize that an electric one-form symmetry is entirely responsible for protecting the potential of axions arising from 5D gauge theories and use this to systematically characterize the extra-dimensional axion quality problem. We identify three ways of breaking this one-form symmetry to generate an axion potential: adding electrically charged matter, gauging a magnetic higher-form symmetry, and turning on an ABJ anomaly. In the latter case, we identify new ways of generating an axion potential via extra-dimensional magnetic monopoles. We also discuss how the axion is modified if the protective electric one-form symmetry is itself gauged. Finally, we relate these effects to gravitational expectations for the quality problem via generalized weak gravity conjectures. The clarity that generalized symmetries bring to the extra-dimensional axion quality problem highlights their relevance to particle phenomenology.