# Anomalous electrodynamics of neutral pion matter in strong magnetic fields

## TL;DR

This paper explores the complex electromagnetic excitations in neutral pion matter under strong magnetic fields, revealing unique mixed modes, a gapped neutral-pion-like mode, and stability against certain instabilities, with implications for quantum chromodynamics.

## Contribution

It introduces a novel analysis of photon-pion mixing and excitation modes in the chiral soliton lattice of neutral pions in strong magnetic fields, including the discovery of a nonrelativistic gapless mode.

## Key findings

- Identification of two gapped excitations and one gapless mode with nonrelativistic dispersion.
- The gapless mode interpolates between electromagnetic and surface wave behaviors.
- Thermal fluctuations do not cause Landau-Peierls instability but affect pressure scaling.

## Abstract

The ground state of quantum chromodynamics in sufficiently strong external magnetic fields and at moderate baryon chemical potential is a chiral soliton lattice (CSL) of neutral pions. We investigate the interplay between the CSL structure and dynamical electromagnetic fields. Our main result is that in presence of the CSL background, the two physical photon polarizations and the neutral pion mix, giving rise to two gapped excitations and one gapless mode with a nonrelativistic dispersion relation. The nature of this mode depends on the direction of its propagation, interpolating between a circularly polarized electromagnetic wave and a neutral pion surface wave, which in turn arises from the spontaneously broken translation invariance. Quite remarkably, there is a neutral-pion-like mode that remains gapped even in the chiral limit, in seeming contradiction to the Goldstone theorem. Finally, we have a first look at the effect of thermal fluctuations of the CSL, showing that even the soft nonrelativistic excitation does not lead to the Landau-Peierls instability. However, it leads to an anomalous contribution to pressure that scales with temperature and magnetic field as $T^{5/2}(B/f_\pi)^{3/2}$.