The Chiral Magnetic Effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory

We study some properties of the non-Abelian vacuum induced by strong external magnetic field. For this purpose we use the quenched SU(3) lattice gauge theory with tadpole-improved Luscher-Weisz action and chirally invariant lattice Dirac operator. Within this approach the following results have been obtained: The chiral symmetry breaking is enhanced by the magnetic field. The corresponding chiral condensate depends on the field as a function of power n = 1.6 +/- 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties have been calculated and compared with theoretical estimations. Finally, there are non-zero local fluctuations of the both chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be recognized as an evidence of the Chiral Magnetic Effect (CME), which is observed by the STAR Collaboration in heavy ion collisions at RHIC