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 AΛ _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|≳(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.