We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon (B), strangeness (S), electric charge (Q), and isospin (I) chemical potentials µ X=B,Q,S,I . The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as (0)) 4 , we determined κ X 2 and κ X 4 from Taylor expansions of chiral observables in µ X . We obtained a precise result for T c (0) = (156.5 ± 1.5) MeV. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., µ S (T, µ B ) and µ Q (T, µ B ) fixed from strangeness-neutrality and isospin-imbalance, we found κ B 2 =0.012(4) and κ B 4 =0.000(4). For µ B 300 MeV, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of 0.42(6) GeV/fm 3 and constant entropy density of 3.7(5) fm −3 .

We investigate the Dirac eigenvalue spectrum (𝜌(𝜆, 𝑚 𝑙 )) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives (𝜕 𝑛 𝜌(𝜆, 𝑚 𝑙 )/𝜕𝑚 𝑛 𝑙 ) of the Dirac eigenvalue spectrum with respect to the quark mass (𝑚 𝑙 ) and the (𝑛+1)-point correlations among the eigenvalues (𝜆) of the massless Dirac operator. Based on these relations, we present lattice QCD results for 𝜕 𝑛 𝜌(𝜆, 𝑚 𝑙 )/𝜕𝑚 𝑛 𝑙 (𝑛 = 1, 2, 3) with 𝑚 𝑙 corresponding to pion masses 𝑚 𝜋 = 160 − 55 MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1)-flavors of highly improved staggered quarks and the tree-level Symanzik gauge action with the physical strange quark mass, three lattice spacings 𝑎 = 0.12, 0.08, 0.06 fm, and lattices having aspect ratios 4 − 9. We find that 𝜌(𝜆 → 0, 𝑚 𝑙 ) develops a peaked structure. This peaked structure, which arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as 𝑎 → 0, and its amplitude is proportional to 𝑚 2 𝑙 . After continuum and chiral extrapolations, we find that the axial anomaly remains manifested in two-point correlation functions of scalar and pseudo-scalar mesons in the chiral limit. We demonstrate that the behavior of 𝜌(𝜆 → 0, 𝑚 𝑙 ) is responsible for it.

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