Exploring the axion potential and axion walls in dense quark matter

We study the potential of the Quantum Chromodynamics axion in hot and/or dense quark matter, within a Nambu-Jona-Lasinio-like model that includes the coupling of the axion to quarks. Differently from previous studies, we implement local electrical neutrality and $\beta-$equilibrium, which are relevant for the description of the quark matter in the core of compact stellar objects. Firstly we compute the effects of the chiral crossover on the axion mass and self-coupling. We find that the low energy properties of axion are very sensitive to the phase transition of Quantum Chromodynamics, in particular, when the bulk quark matter is close to criticality. Then, for the first time in the literature we compute the axion potential at finite quark chemical potential and study the axion domain walls in bulk quark matter. We find that the energy barrier between two adjacent vacuum states decrease in the chirally restored phase: this results in a lower surface tension of the walls. Finally, we comment on the possibility of production of walls in dense quark matter.