Axions and their physics: from tabletops to cosmology and back again?

I introduce the general idea of axions: particles associated to fields which are valued on a circle rather than a real line. I describe the still unresolved strong CP problem of the Standard Model, for which the so-called QCD axion provides the most plausible solution. I explain the typical coupling of particle physics axions to electromagnetism and how this leads to axion-photon conversion in magnetic fields and potential search strategies for axions.

Over the past decade, topological ideas have played an increasingly important role in a surprising setting: the problem of understanding the properties of insulating crystals. This has led to the identification of “topological insulators”, bulk insulating materials which are characterised by unusual surface phenomena, unconventional responses to applied electric and magnetic fields, or both. In particular, the motion of electrons in some three-dimensional solids can generate axion-like electrodynamics in the solid state. I will explain how the ideas leading to the prediction of this “axion insulator” flow naturally from a deeper understanding of the electrodynamics of dielectric media and their link to topological ideas, and survey some of their unusual consequences for experiment.

The QCD-axion, and its `axion-like-particle' generalisations, lead to new physical effects in an extraordinarily diverse range of settings including cosmology, astrophysical objects like stars and black holes, electromagnetic systems, atoms, molecules, and nuclei. I outline how this leads to a correspondingly huge range of search possibilities for axions (and even axion dark matter) varying from those involving observations of solar-mass and supermassive black holes and a form of `gravitational atom’, to many current and near future ultra-precise quantum `table top' experiments in the Beecroft basement and others worldwide.