Anomalous massless modes

TL;DR

This paper explores the existence of anomalous massless modes in various dimensions, linking them to anomaly-induced effects like Schwinger terms, and identifies their physical manifestations such as charge density waves and chiral magnetic waves.

Contribution

The paper reinterprets the analogy of anomalous massless modes and demonstrates their universal emergence due to anomaly-induced Schwinger terms across different dimensions.

Findings

In 1+1 dimensions, the mode corresponds to charge density waves in Luttinger liquids.

In 3+1 dimensions, the mode is identified as the chiral magnetic wave.

Both modes originate from the same underlying anomaly physics.

Abstract

Some years ago Anton Yu. Alekseev et al. conjectured the existence of massless modes in the spectrum of excitations ("anomalous massless modes") building upon certain similarities between a spontaneous symmetry breaking and the interplay of axial and vector symmetries in an anomalous theory. We reinterpret the analogy and argue that the presence of these modes is ensured in any (even) number of dimensions only by the excitation of certain anomaly-induced terms called Schwinger terms. In 1+1 dimensions the anomalous massless mode corresponds to the charge density wave present in a Luttinger liquid. In 3+1 dimensions, we identify the anomalous massless mode with the so-called chiral magnetic wave. Our analysis shows that both modes arise as a consequence of the same physics.