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 ω ∼ 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.

Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics

“…One is to analyze physics in the background magnetic field, spatially varying axion field, and so on. It has been shown that in non-trivial backgrounds, mass spectra of the axion and photon are deformed [26,54,55,116]. We may understand such deformations of the phase structure by using higher-form symmetries, 3group, and their 't Hooft anomalies (see e.g., ref.…”

“…For example, we can understand photons in the pure Maxwell theory as Nambu-Goldstone bosons [42,52,53]. Such an interpretation has been generalized to non-relativistic cases as well [26,[54][55][56]. Here, a charged object is a 1-dimensional Wilson loop whose vacuum expectation value is finite in the Coulomb phase.…”

Effective description of non-equilibrium currents in cold magnetized plasma

“…For concreteness, in the remainder of this paper we will work with the specific theory given by (39), where the FFE sector is given by the choice…”

Field theories with higher-group symmetry from composite currents

“…Thanks to the fact that local conservation laws govern small departures from thermodynamic equilibrium, continuous higher-form symmetries have found natural applications to magnetohydrodynamics [19][20][21][22] and to the effective field theory (EFT) description of systems with topological defects [23,24]. Finally, it has been pointed out [25,26] that the spectrum of Nambu-Goldstone (NG) bosons arising from spontaneously broken higher-form symmetries in nonrelativistic systems features subtleties, analogous to those found for spontaneously broken 0-form symmetries, see refs. [27][28][29] for recent reviews.…”