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

Abstract

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 π 0→ 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 N c —the number of quark colors. The magnon analogue of this prefactor is the anyon statistics angle θ which need not be quantized.