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. We perform calculations in the quenched SU(3) lattice gauge theory with tadpole-improved Luscher-Weisz action and chirally invariant lattice Dirac operator. The following results are obtained: The chiral symmetry breaking is enhanced by the magnetic field. The chiral condensate depends on the strength of the applied field as a power function with exponent n = 1.6 +/- 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties are calculated and compared with the theoretical estimations. There are non-zero local fluctuations of the chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be a manifestation of the Chiral Magnetic Effect (CME).