Magnetic catalysis and anisotropic confinement in QCD

Abstract

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 $N^{thr}_c$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c \ll N^{thr}_c$, 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 $N^{thr}_c$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N^{thr}_c$ grows rapidly with the magnetic field [$N^{thr}_c \gtrsim 100$ for $|eB| \gtrsim (1{GeV})^2$]. In contrast to QCD with a nonzero baryon density, there are no principal obstacles for checking these results and predictions in lattice computer simulations.