In the chiral symmetric phase, the polarized instanton–anti-instanton molecule pairing induces a nontrivial repulsive interaction in the isoscalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration phase, there is a first order phase transition for the spontaneous generation of local charge parity ($\mathcal{C}\mathcal{P}$) violation and chirality imbalance. Furthermore, it is found that external magnetic fields will lower the critical temperature for the local $\mathcal{C}\mathcal{P}$-odd phase transition and catalyze the chirality imbalance, which destroys the chiral condensate with pairing quarks between different chiralities. A reasonable strength of the repulsive interaction in the isoscalar axial-vector channel can naturally explain the inverse magnetic catalysis around the critical temperature under external magnetic fields.

• Received 8 June 2014

DOI:https://doi.org/10.1103/PhysRevD.90.074009