The chiral magnetic effect is the generation of electric current of quarks along external magnetic field in the background of topologically nontrivial gluon fields. There is a recent evidence that this effect is observed by the STAR Collaboration in heavy ion collisions at RHIC. In our paper we study qualitative signatures of the chiral magnetic effect using quenched lattice simulations. We find indications that the electric current is indeed enhanced in the direction of the magnetic field both in equilibrium configurations of the quantum gluon fields and in a smooth gluon background with nonzero topological charge. In the confinement phase the magnetic field enhances the local fluctuations of both the electric charge and chiral charge densities. In the deconfinement phase the effects of the magnetic field become smaller, possibly due to thermal screening. Using a simple model of a fireball we obtain a good agreement between our data and experimental results of the STAR Collaboration.Comment: 14 pages, 14 figures, uses RevTeX 4.0; revision: references and comments added, figures corrected, published versio

We study the correlator of two vector currents in quenched SU (2) lattice gauge theory with a chirally invariant lattice Dirac operator with a constant external magnetic field. It is found that in the confinement phase the correlator of the components of the current parallel to the magnetic field decays much slower than in the absence of a magnetic field, while for other components the correlation length slightly decreases. We apply the maximal entropy method to extract the corresponding spectral function. In the limit of zero frequency this spectral function yields the electric conductivity of the quenched theory. We find that in the confinement phase the external magnetic field induces nonzero electric conductivity along the direction of the field, transforming the system from an insulator into an anisotropic conductor. In the deconfinement phase the conductivity does not exhibit any sizable dependence on the magnetic field.PACS numbers: 11.30. Rd; 12.38.Gc; Recently, heavy ion experiments at the BNL Relativistic Heavy Ion Collider (RHIC) have found an evidence [1] for the so-called chiral magnetic effect [2] in quarkgluon plasma. The essence of the effect is the generation of electric current along the direction of the external magnetic field in the background of topologically nontrivial gauge field configurations. Experimentally, the effect manifests itself as the dynamical enhancement of fluctuations in the numbers of charged hadrons emitted above and below the reaction plane in off-central heavyion collisions. Recently this effect has been studied also in lattice gauge theory, and the evidence for charge separation in magnetic field has been found [3,5]. In [3] it has been found that the fluctuations of the electric current along the magnetic field are strongly enhanced as compared to the fluctuations of current in the perpendicular directions. This conclusion was also confirmed by an analytical calculation in the instanton gas model [6]. The result of [3] on the difference of longitudinal and transverse electric current susceptibilities has been reproduced later by an analytical calculation [7]; the frequency dependence of the conductivity has also been evaluatedfor the weak coupling result, see [8].A natural question to ask is whether this enhancement of current fluctuations corresponds to a real flow of charge, or is just caused by short-lived quantum fluctuations. This question can be answered by studying the current-current correlation functions. The currents which correspond to a real transport of charged particles should have long-range correlations in time, while quantum fluctuations are typically characterized by a finite correlation time [9]. Recalling Green-Kubo relations, one can see that this property is intimately related to the electric conductivity -namely, the real transport of charged particles can occur only in conducting media.

5 pages RevTeX, 5 figuresInternational audienceWe investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in quenched SU(2) gauge theory on the lattice. In agreement with the predictions of the chiral perturbation theory, the chiral condensate grows linearly with the field strength up to (e B)^(1/2) = 1.5 GeV. In the background magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger Hausdorf dimensionality. This delocalization increases the degeneracy of near-zero eigenmodes, and, according to the Banks-Casher relation, enhances the chiral symmetry breaking

We report on the direct numerical measurements of the conductivity of graphene monolayer. Our numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. The conductivity is obtained from the Green-Kubo relations using the Maximum Entropy Method. We find that in a phase with spontaneously broken sublattice symmetry the conductivity rapidly decreases. For the largest value of the coupling constant used in our simulations g = 4.5, the DC conductivity is less than the DC conductivity in the weak-coupling phase (at g < 3.5) by at least three orders of magnitude.

We investigate the masses (ground state energies) of neutral pseudoscalar and vector meson in SU (3) lattice gauge theory in strong abelian magnetic field. The energy of ρ 0 meson with zero spin projection sz = 0 on the axis of the external magnetic field decreases, while the energies with nonzero spins sz = −1 and +1 increase with the field. The energy of π 0 meson decrease as a function of the magnetic field. We calculated the magnetic polarizabilities of pseudoscalar and vector mesons for lattice volume 18 4 . For ρ 0 with spin |sz| = 1 and π 0 meson the extrapolations to zero lattice spacing have been done. We do not observe any evidence in favour of tachyonic mode existence.