Abstract
In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $\omega \sim k^2$ and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a possible realization of such nonrelativistic NG modes in 3-dimensional Dirac semimetals.
Highlights
Spontaneous symmetry breaking (SSB) is one of the most important notions in modern physics that explains various physical phenomena from superfluidity to the origin of hadron masses
Whether an NG mode has the linear or quadratic dispersion relation is classified by the quantity ρab ≡ h1⁄2Qa; Qbi ≠ 0, with Qa broken symmetry generators and the expectation value taken in the vacuum: the NG mode characterized by nonvanishing ρab typically has the quadratic dispersion relation and is called type-B, while the rest typically has the linear dispersion relation and is called type
We show that the emergence of the type-B NG mode of generalized global symmetries is more generic than previously thought and it appears in a much more simple setup: strongly interacting massless Dirac fermions coupled to a dynamical U(1) gauge field in a background magnetic field
Summary
Spontaneous symmetry breaking (SSB) is one of the most important notions in modern physics that explains various physical phenomena from superfluidity to the origin of hadron masses. It has been shown that photons with the quadratic dispersion relation (or nonrelativistic photons) appear in the axion electrodynamics with a spatially varying and periodic θ term and that it may be interpreted as a type-B NG mode [12,13]. Such a situation is expected to be realized in dense nuclear or quark matter in a magnetic field [12,14] and a periodic array of topological and normal insulators [15] As we shall discuss, this type-B NG mode should be experimentally testable, e.g., in Dirac semimetals in 3-dimensional solids
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