Magnetic catalysis and anisotropic confinement in QCD

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors N_c^thr, dividing the theories with essentially different dynamics, is established. For the number of colors N_c≪N_c^thr, an anisotropic dynamics of confinement with the confinement scale much less than Λ_QCD and a rich spectrum of light glueballs is realized. For N_c of order N_c^thr or larger, a conventional confinement dynamics takes place. It is found that the threshold value N_c^thr grows rapidly with the magnetic field [N_c^thr≳100 for |eB|≳(1GeV)²]. In contrast with QCD with a nonzero baryon density, there are no principal obstacles for examining these results and predictions in lattice computer simulations.