Pions versus magnons: from QCD to antiferromagnets and quantum Hall ferromagnets Original Research Article

The low-energy dynamics of pions and magnons—the Goldstone bosons of the strong interactions and of magnetism—are analogous in many ways. The electroweak interactions of pions result from gauging an SU(2)L⊗U(1)Y symmetry which then breaks to the U(1)em gauge symmetry of electromagnetism. The electromagnetic interactions of magnons arise from gauging not only U(1)em but also the SU(2)s spin rotational symmetry, with the electromagnetic fields E→ and B→ appearing as non-Abelian vector potentials. Pions couple to electromagnetism through a Goldstone–Wilczek current that represents the baryon number of Skyrmions and gives rise to the decay π0→γγ. Similarly, magnons may couple to an analogue of the Goldstone–Wilczek current for baby-Skyrmions which induces a magnon–two-photon vertex. The corresponding analogue of photon–axion conversion is photon–magnon conversion in an external magnetic field. The baryon number violating decay of Skyrmions can be catalyzed by a magnetic monopole via the Callan–Rubakov effect. Similarly, baby-Skyrmion decay can be catalyzed by a charged wire. For more than two flavors, the Wess–Zumino–Witten term enters the low-energy pion theory with a quantized prefactor Nc—the number of quark colors. The magnon analogue of this prefactor is the anyon statistics angle θ which need not be quantized.