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Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors

It was recently conjectured that, in SU(3) gauge theories with fundamental quarks, valence spontaneous chiral symmetry breaking is equivalent to condensation of local dynamical chirality and appearance of chiral polarization scale $Λ_{ch}$. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width ($Λ_{ch}$), is also characterized by volume density of participating modes ($Ω$) and the volume density of total chirality ($Ω_{ch}$). Few possible forms of the correspondence are discussed, paying particular attention to singular cases where $Ω$ emerges as the most versatile characteristic. The notion of finite-volume "order parameter", capturing the nature of these connections, is proposed. We study the effects of temperature (in N$_f$=0 QCD) and light quarks (in N$_f$=12), both in the regime of possible symmetry restoration, and find agreement with these ideas. In N$_f$=0 QCD, results from several volumes indicate that, at the lattice cutoff studied, the deconfinement temperature $T_c$ is strictly smaller than the overlap-valence chiral transition temperature $T_{ch}$ in real Polyakov line vacuum. Somewhat similar intermediate phase (in quark mass) is also seen in N$_f$=12. It is suggested that deconfinement in N$_f$=0 is related to indefinite convexity of absolute X-distributions.