Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries

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.

arXiv comment6 pages; v2: published version

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Cited by in corpus (16)

• Generalized Symmetries in Condensed Matter
• Counting Rules of Nambu-Goldstone Modes
• Higher-form symmetries and 3-group in axion electrodynamics
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Counting Nambu-Goldstone modes of higher-form global symmetries
• Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
• Field theories with higher-group symmetry from composite currents
• Effective Field Theory for Spontaneously Broken Symmetry
• Electrical neutrality and $\beta$-equilibrium conditions in dense quark matter: generation of charged pion condensation by chiral imbalance
• Generalized chiral instabilities, linking numbers, and non-invertible symmetries
• Topological mass generation in gapless systems
• Effective description of non-equilibrium currents in cold magnetized plasma
• Unstable Nambu-Goldstone modes
• Novel dynamic critical phenomena induced by superfluidity and the chiral magnetic effect in Quantum Chromodynamics
• Anomalous Dynamical Screening of Relativistic Plasma in a Magnetic Field
• Effective field theory for dissipative photons from higher-form symmetries