Quark mass dependence of the vacuum electric conductivity induced by the magnetic field in SU(2) lattice gluodynamics

We study the electric conductivity of the vacuum of quenched SU(2) lattice gauge theory induced by the magnetic field B as a function of the bare quark mass m. The conductivity grows as the quark mass decreases. Simplest power-like fit indicates that the conductivity behaves as B/sqrt(m). We discuss the implications of this result for dilepton angular distributions in heavy ion collisions.Comment: 5 pages RevTeX, 4 figure

Entanglement entropy in lattice gauge theories

We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux. For SU(2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.Comment: Talk presented at the Confinement8 conference (Mainz, Germany, September 1 - 6, 2008) and at the conference "Liouville Field Theory and Statistical Models", dedicated to Alexey Zamolodchikov memory (Moscow, Russia, June 21 - 24, 2008

Numerical evidence of chiral magnetic effect in lattice gauge theory

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

Heavy quark potential in lattice QCD at finite temperature

Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for m_{\pi}/m_{\rho} \sim 0.8 and lattice spacing a \sim 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase.Comment: 3 pages, 1 figure, talk given at the 5th International Conference on Quark Confinement and the Hadron Spectrum, Gargnano, Italy, 10-14 Sep 200

Quantum Theory of Strings in Abelian Higgs Model

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.Comment: 17 pages, LaTe

Finite Temperature QCD with Two Flavors of Non-perturbatively Improved Wilson Fermions

We study QCD with two flavors of non-perturbatively improved Wilson fermions at finite temperature on the $16^3 8$ lattice. We determine the transition temperature at lattice spacings as small as $a \sim 0.12$ fm, and study string breaking below the finite temperature transition. We find that the static potential can be fitted by a two-state ansatz, including a string state and a two-meson state. We investigate the role of Abelian monopoles at finite temperature.Comment: 29 pages, 22 figures, Late

Gauge invariant structures and Confinement

By looking at cooled configurations on the lattice, we study the presence of peaks in the action density, or its electric and magnetic components, in the SU(2) gauge vacuum. The peaks are seen to be of instanton-like nature and their number variation takes care of the drop in the string tension observed when cooling. Possible explanations of this finding are analysed.Comment: uuencoded and compressed file of the Postcript file newpaper.ps, fig1.ps,fig2.eps,fig3.ps and fig4.ps. 13 pages of text and 4 figures Style modifications and misprints correcte