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 Ncᵗʰʳ, dividing the theories with essentially different dynamics, is established. For the number of colors NcNcᵗʰʳ, an anisotropic dynamics of confinement with the confinement scale much less than ΛQCD and a rich spectrum of light glueballs is realized. For Nc of order Ncᵗʰʳ or larger, a conventional confinement dynamics takes place. It is found that the threshold value Ncᵗʰʳ grows rapidly with the magnetic field [Ncᵗʰʳ100 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.