M. I. Polikarpov

Magnetic-field-induced insulator-conductor transition in SU(2) quenched lattice gauge theory.

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 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.

Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field

Abstract We investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in SU ( 2 ) Yang–Mills theory on the lattice. We observe that the chiral condensate grows linearly with the field strength B up to e B = 3 GeV as predicted by chiral perturbation theory for full QCD. As the temperature increases the coefficient in front of the linear term gets smaller. In the magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger (compared to zero-field case) Hausdorff dimensionality. We suggest that the delocalization of near-zero eigenmodes plays a crucial role in the enhancement of the chiral symmetry breaking.

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 Lüscher-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 ν = 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 nonzero 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.

Chiral magnetization of non-Abelian vacuum: A Lattice study

Abstract The chiral magnetization properties of cold and hot vacua are studied using quenched simulations in lattice Yang–Mills theory. In weak external magnetic fields the magnetization is proportional to the first power of the magnetic field. We evaluate numerically the coefficient of the proportionality (the chiral susceptibility) using near-zero eigenmodes of overlap fermions. We found that the product of the chiral susceptibility and the chiral condensate equals to 46 ( 3 ) MeV . This value is very close to the phenomenological value of 50 MeV . In strong fields the magnetization is a nonlinear function of the applied magnetic field. We find that the nonlinear features of the magnetization are well described by an inverse tangent function. The magnetization is weakly sensitive to temperature in the confinement phase.

Quark electric dipole moment induced by magnetic field

We show numerically that quarks develop an electric dipole moment in the direction of a sufficiently intense magnetic field due to local fluctuations of topological charge. This anomalous CP-odd effect is a spin analogue of the chiral magnetic effect in QCD.

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. In this review, written for a memorial volume dedicated to the memory of Academician A.B. Migdal, we emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. We emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.

Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics

DESY, Notkestrasse 85, 22607 Hamburg, Germany(Dated: December 3, 2011)We study the effect of cooling on the spatial distribution of the topological charge density inquenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field con-figurations are cooled, the Hausdorff dimension of regions where the topological charge is localizedgradually changes from d = 2 ÷3 towards the total space dimension. Hence the cooling proceduredestroys some of the essential properties of the topological charge distribution.

Numerical study of chiral magnetic effect in quenched SU(2) lattice gauge theory

A possible experimental observation of the chiral magnetic effect in heavy ion collisions at RHIC was recently reported by the STAR Collaboration. We study signatures of this effect in SU(2) lattice gluodynamics with the chirally invariant Dirac operator. We find that at zero temperature the local fluctuations of an electric current of quarks and chirality fluctuations increase with external Abelian magnetic field. The external magnetic field leads to spatial separation of the quarks electric charges. The separation increases with the strength of the magnetic field. As temperature gets higher the dependence of these quantities on the strength of the magnetic field becomes weaker. In the deconfinement phase the local fluctuations of the chiral density and of the spatial components of the quarks electric current are large and are almost independent on the external magnetic field. The local fluctuations of the electric charge density decrease with the strength of the magnetic field in this phase.

Finite temperature phase transition with two flavors of improved Wilson fermions

The critical temperature is computed for N f = 2 dynamical flavors of nonperturbatively improved Wilson fermions. The new simulations are performed on lattices 403x14 with lattice spacing and pion mass about 0.08 fm and 200 MeV, respectively. We find the deconfinement and chiral phase transitions to coincide within numerical precision. Our results are in broad agreement with a second order phase transition in the chiral limit. The critical temperature at the physical quark mass is found to be Tc = 172(3)(6)MeV.

Topological and magnetic properties of the QCD vacuum probed by overlap fermions

We study some of the local CP-odd and magnetic properties of the non-Abelian vacuum with use of overlap fermions within the quenched lattice gauge theory. Among these properties are the following: inhomogeneous spatial distribution of the topological charge density (chirality for massless fermions) in SU(2) gluodynamics (for uncooled gauge configurations the chirality is localized on low-dimensional defects with d=2..3, while a sequence of cooling steps gives rise to four-dimensional instantons and hence a four-dimensional structure of the chirality distribution); finite local fluctuations of the chirality growing with the strength of an external magnetic field; magnetization and susceptibility of the QCD vacuum in SU(3) theory; magnetic catalysis of the chiral symmetry breaking, and the electric conductivity of the QCD vacuum in strong magnetic fields.