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

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The entropy of entanglement between a three-dimensional slab of thickness l and its complement is studied numerically for four-dimensional SU (2) lattice gauge theory. We find a signature of a nonanalytic behavior of the entanglement entropy, which was predicted recently for large Nc confining gauge theories in the framework of AdS/CFT correspondence. The derivative of the entanglement entropy over l is likely to have a discontinuity at some l = lc. It is argued that such behavior persists even at finite temperatures, probably turning into a sort of crossover for temperatures larger than the temperature of the deconfinement phase transition. We also confirm that the entanglement entropy contains quadratically divergent l-independent term, and that the nondivergent terms behave as l −2 at small distances.

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.

We report measurements of the action associated with center vortices in SU(2) pure lattice gauge theory. In the lattice units the excess of the action on the plaquettes belonging to the vortex is approximately a constant, independent on the lattice spacing 'a'. Therefore the action of the center vortex is of order 'A/a^2', where 'A' is its area. Since the area 'A' is known to scale in the physical units, the measurements imply that the suppression due to the surface action is balanced, or fine tuned to the entropy factor which is to be an exponential of 'A/a^2'.Comment: Version accepted for publication in PLB, stylistic change

Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov-Nielsen-Olesen strings. It is shown that in four space -time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov-Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the theory. We show that the Aharonov-Bohm effect gives rise to several nontrivial commutation relations.

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