Axial-anomaly effects and chiral phase structure in holographic QCD

Abstract

We study the impact of axial-anomaly effects on the chiral phase structure in a $U(3)$-extended soft-wall holographic QCD model. Including the pseudoscalar singlet sector allows for a dynamical description of the $η$-$η^\prime$ system through a determinant interaction with a holographic-coordinate-dependent strength. Vacuum pseudoscalar observables, particularly the $η^\prime$ mass and the $η$-$η^\prime$ mixing pattern, constrain the overall magnitude of the anomaly contribution but leave its holographic profile largely undetermined. We then examine how different anomaly profiles consistent with vacuum phenomenology affect the finite-temperature chiral transition. Constructing the Columbia plot within this framework, we find that the predicted phase structure depends sensitively on the anomaly implementation: some profiles yield crossover/second-order behavior across the entire quark-mass plane, while others generate a first-order region in the light-quark corner. These results highlight the strong sensitivity of the holographic QCD phase structure to the modeling of axial-anomaly effects.

Figures (8)

• Figure 1: Radial trajectories of the pseudoscalar mesons for the three anomaly profiles (A, B, and C). Solid curves denote model predictions, while black points show experimental masses from Ref. ParticleDataGroup:2024cfk. Red points indicate tentative states (marked by $\dagger$ in Table \ref{['tab: pseudo spectrum']}).
• Figure 2: Radial wavefunctions of the singlet ($0$) and octet ($8$) pseudoscalar components for the $\eta$ and $\eta^\prime$ states obtained with different anomaly profiles.
• Figure 3: Dependence of $m_{\eta}^2$ and $m_{\eta'}^2$ on $m_\pi^2$ along a fixed strange-quark-mass trajectory for representative anomaly-profile parameter sets. Red error bars and gray bands denote lattice-QCD results from Ref. Ottnad:2025zxq.
• Figure 4: Radial trajectories of pseudoscalar and scalar mesons from the simultaneous scalar-pseudoscalar fit with the Type-B anomaly profile. Solid curves denote model predictions and points show experimental masses from Ref. ParticleDataGroup:2024cfk. Red points indicate tentative states (marked by $\dagger$ in Table \ref{['tab: ScalarSpectra']}).
• Figure 5: Radial wavefunctions of the singlet ($a=0$) and octet ($a=8$) components for the two lowest pseudoscalar and scalar eigenstates in the coupled singlet-octet ($0$-$8$) sector.