Axions: From Heaven to Earth

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Axions are hypothetical particles whose existence would solve two major problems: the strong P, T problem (a major blemish on the standard model); and the dark matter problem. It is a most important goal to either observe or rule out the existence of a cosmic axion background. It appears that decisive observations may be possible, but only after orchestrating insight from specialities ranging from quantum field theory and astrophysical modeling to ultra-low noise quantum measurement theory. Detailed predictions for the magnitude and structure of the cosmic axion background depend on cosmological and astrophysical modeling, which can be constrained by theoretical insight and numerical simulation. In parallel, we must optimize strategies for extracting accessible signals from that very weakly interacting source. While the existence of axions as fundamental particles remains hypothetical, the equations governing how axions interact with electromagnetic fields also govern (with different parameters) how certain materials interact with electromagnetic fields. Thus those materials embody “emergent” axions. The equations have remarkable properties, which one can test in these materials, and possibly put to practical use. Closely related to axions, mathematically, are anyons. Anyons are particle-like excitations that elude the familiar classification into bosons and fermions. Theoretical and numerical studies indicate that they are common emergent features of highly entangled states of matter in two dimensions. Recent work suggests the existence of states of matter, both natural and engineered, in which anyon dynamics is both important and experimentally accessible. Since the equations for anyons and axions are remarkably similar, and both have common, deep roots in symmetry and topology, it will be fruitful to consider them together.