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.

6 pages; v2: published version

References in corpus (8)

• The Chiral Magnetic Effect
• Generalized Global Symmetries
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• On electrodynamics of chiral matter
• Anomalous electrodynamics of neutral pion matter in strong magnetic fields
• Stability of Multinode Dirac Semimetals against Strong Long-Range Correlations
• Anomalous low-temperature thermodynamics of QCD in strong magnetic fields
• Monte-Carlo study of Dirac semimetals phase diagram

Cited by in corpus (9)

• Generalized Symmetries in Condensed Matter
• Higher-form symmetries and 3-group in axion electrodynamics
• Field theories with higher-group symmetry from composite currents
• Effective Field Theory for Spontaneously Broken Symmetry
• Generalized chiral instabilities, linking numbers, and non-invertible symmetries
• Unstable Nambu-Goldstone modes
• Effective field theory for dissipative photons from higher-form symmetries
• 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