Anomalous Axion Interactions and Topological Currents in Dense Matter

TL;DR

The paper addresses how chiral anomalies induce topological, non-dissipative currents in dense matter under magnetic fields, notably an axial current on magnetic flux tubes and a Peccei–Quinn current for axions. It derives an anomalous axion Lagrangian by extending the anomaly-based effective framework to include the axion field, predicting a current proportional to the magnetic flux in a dense medium: $J = \frac{N_c \sum_a e_a \mu_a Q_a}{2 \pi^2} \Phi$ for the axial case and $J^{PQ} = \sum_a \frac{e_a \mu_a Q_a^{PQ}}{2 \pi^2} \Phi$ for the axion-related current. The authors provide three complementary derivations—anomaly-based effective Lagrangians, a 3+1D anomaly approach, and a microscopic zero-mode calculation—validating the results and highlighting their topological character and independence from $f_a$. They discuss potential astrophysical implications, especially neutron-star kicks, and outline broader implications for axion phenomenology and dense-matter dynamics.

Abstract

Recently an effective Lagrangian for the interactions of photons, Nambu-Goldstone bosons and superfluid phonons in dense quark matter has been derived using anomaly matching arguments. In this paper we illuminate the nature of certain anomalous terms in this Lagrangian by an explicit microscopic calculation. We also generalize the corresponding construction to introduce the axion field. We derive an anomalous axion effective Lagrangian describing the interactions of axions with photons and superfluid phonons in the dense matter background. This effective Lagrangian, among other things, implies that an axion current will be induced in the presence of magnetic field. We speculate that this current may be responsible for the explanation of neutron star kicks.