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

## TL;DR

This paper explores how triangle anomalies induce nonrelativistic Nambu-Goldstone modes in systems with generalized global symmetries, linking theoretical predictions to potential realizations in Dirac semimetals.

## Contribution

It demonstrates that gapless modes in massless QCD coupled to QED under magnetic fields are type-B NG modes arising from anomalies, providing a new interpretation of these modes.

## Key findings

- Identification of a gapless mode as a type-B NG mode
- Connection between anomalies and nonrelativistic NG modes
- Potential realization in Dirac semimetals

## 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.