Magnetic Catalysis vs Magnetic Inhibition

We discuss the fate of chiral symmetry in an extremely strong magnetic field B. We investigate not only quark fluctuations but also neutral meson effects. The former would enhance the chiral-symmetry breaking at finite B according to the Magnetic Catalysis, while the latter would suppress the chiral condensate once B exceeds the scale of the hadron structure. Using a chiral model we demonstrate how neutral mesons are subject to the dimensional reduction and the low dimensionality favors the chiral-symmetric phase. We point out that this effect, the Magnetic Inhibition, can be a feasible explanation for recent lattice-QCD data indicating the decreasing behavior of the chiral-restoration temperature with increasing B.