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 ${N}_{c}^{\mathrm{thr}},$ dividing the theories with essentially different dynamics, is established. For the number of colors ${N}_{c}\ensuremath{\ll}{N}_{c}^{\mathrm{thr}},$ an anisotropic dynamics of confinement with the confinement scale much less than ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$ and a rich spectrum of light glueballs is realized. For ${N}_{c}$ of order ${N}_{c}^{\mathrm{thr}}$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value ${N}_{c}^{\mathrm{thr}}$ grows rapidly with the magnetic field $[{N}_{c}^{\mathrm{thr}}\ensuremath{\gtrsim}100$ for $|\mathrm{eB}|\ensuremath{\gtrsim}(1\mathrm{GeV}{)}^{2}].$ In contrast with QCD with a nonzero baryon density, there are no principal obstacles for examining these results and predictions in lattice computer simulations.