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Anomalous massless modes

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.