The fact that magnetic fields enhance the chiral symmetry breaking has been known as magnetic catalysis.
Recent lattice studies indicate that the QCD transition temperature decreases for increasing magnetic fields,
which is however not in line with expectations from magnetic catalysis. In this talk, I will discuss the role of
dynamical gluons in the study of the quark mass gap, emphasizing the characteristics of QCD from QED and
effective models (such as the NJL type). The linear rising behavior of the chiral condensate at large magnetic
fields, which has been observed on the lattice, is emerged when nonperturbative gluons are considered.
The result is utilized to interpret the reduction of the transition temperature at large magnetic fields.