Chiral anomaly in (1+1) dimensions revisited: complementary kinetic perspective and universality

TL;DR

This paper revisits the (1+1)-dimensional chiral anomaly, showing it can emerge without Berry curvature corrections and demonstrating its universality across different quasiparticle dispersions using kinetic theory and current algebra.

Contribution

It introduces a kinetic theory reformulation of the chiral anomaly and proves its universality for various quasiparticle dispersions in (1+1) dimensions.

Findings

Chiral anomaly can occur without Berry curvature corrections.

Universality of the anomaly across different quasiparticle dispersions.

A monotonic chirality-odd dispersion suffices for the anomaly in two-band models.

Abstract

We reinvestigate the classic example of the chiral anomaly in (1+1) dimensional spacetime. By reviewing the derivation of charge conservation using the semiclassical Boltzmann equation, we show that chiral anomalies could emerge in (1+1) dimensions without Berry curvature corrections to the kinetic theory. The pivotal step depends only on the asymptotic behavior of the distribution function of the quasiparticle--and thus its dispersion relation--in the limit of $\mathbf p\to\pm\infty$ rather than the detailed functional form of the dispersion. We address two subjects motivated by this observation. First, we reformulate (1+1)-dimensional chiral anomaly using kinetic theory with the current algebra approach and the gradient expansion of the Dirac Lagrangian, adding a complementary perspective to existing approaches. Second, we demonstrate the universality of the chiral anomaly across various quasiparticle dispersions. For two-band models linear in the temporal derivative, with Fujikawa's method we show it is sufficient to have a chirality-odd strictly monotonic dispersion in order to exhibit the chiral anomaly.