Axial inverse magnetic catalysis

We find that the inverse magnetic catalysis for $U(1)$ axial symmetry (AIMC: axial inverse magnetic catalysis) can emerge around the chiral crossover regime in the thermomagnetic QCD with 2 + 1 flavors at physical point. This phenomenon can be correlated with the IMC for the chiral $SU(2)_L \times SU(2)_R$ symmetry (CIMC: chiral IMC). We explicitly observe the AIMC based on a Nambu-Jona-Lasinio model with 2 + 1 quark flavors, where introduced anomalous magnetic moments of the quarks play the essential role to drive both the CIMC and AIMC. Our finding is shortly testable on lattices. Possible phenomenological and cosmological implications are also briefly addressed.