Anomalous electrodynamics of neutral pion matter in strong magnetic fields

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 $T^{5/2}(B/f_{\pi }{)}^{3/2}$.

1+22 pages

References in corpus (4)

• Axial anomaly and magnetism of nuclear and quark matter
• On electrodynamics of chiral matter
• Nambu-Goldstone bosons with fractional-power dispersion relations
• Topological interactions of Nambu-Goldstone bosons in quantum many-body systems

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• Quasicrystals in QCD
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Solitonic ground state in supersymmetric theory in background
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• Novel transition dynamics of topological solitons
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Fermionic domain-wall Skyrmions of QCD in a magnetic field
• Constitutive relations of a chiral hadronic fluid