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 $N_c^{thr}$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c\ll N_c^{thr}$, 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 [$N_c^{thr}\gtrsim 100$ for $|eB|\gtrsim (1GeV{)}^2$]. In contrast to QCD with a nonzero baryon density, there are no principal obstacles for checking these results and predictions in lattice computer simulations.

Comments: 10 pages, 1 figure. REVTeX. Minor correction. To appear in Phys. Rev. D