QCD axions and domain walls in dense matter under compact stellar conditions

In compact stellar environments, the stability of dense QCD matter requires the simultaneous fulfillment of charge neutrality and beta equilibrium. In this work, we study how temperature and finite chemical potential affect QCD topology and axion properties within this medium, analyzing both cases with and without the charge neutrality condition. Our results show that the topological susceptibility and axion properties are highly sensitive to the critical behavior of the chiral phase transition in both cases. In particular, the axion mass is strongly suppressed near the transition, while the axion self-coupling constant develops a pronounced peak whose magnitude depends on the temperature and density of the medium. Remarkably, around the critical point at $T\simeq70$ MeV and $\mu\simeq346$ MeV, the self-coupling constant is enhanced by more than a factor of seven compared to its vacuum value, a feature that to the best of our knowledge has not been reported in previous studies. Such a strong amplification at the phase boundary indicates that axion-mediated interactions could play an important role in shaping the structure and stability of compact stars, with potential implications for their evolution and observable astrophysical signatures.