Axial U(1) symmetry in the chiral symmetric phase of 2-flavor QCD at finite temperature

Understand

We discuss the fate of the axial U(1) symmetry in 2-flavor QCD at finite temperature, where the non-singlet chiral symmetry is restored.

• We first summarize the previous theoretical investigation on the relation between the eigenvalue density of the Dirac operator and the axial U(1) symmetry.
• We show that the eigenvalue density near the origin behaves as $\lambda^\gamma$ with $\gamma > 2$ in the chirally symmetric phase, where $\lambda$ is an eigenvalue.
• This implies that the axial U(1) symmetry is partially restored, so that the low energy symmetry of the theory becomes SU(2)$\otimes$ SU(2)$\otimes$ Z$_4$.