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 Lambda(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)greater than or similar to100 for \eB\greater than or similar to(1 GeV)(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.