Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

The spectrum of low-lying eigenvalues of overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T = Tc, though not going to zero. At Tc' = 1.5 Tc = 480 MeV the chiral condensate decreases rapidly one again and becomes either very small or zero. At T < Tc the distributions of small eigenvalues are universal and are well described by chiral orthogonal ensemble of random matrices. In the temperature range above Tc where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton - anti-instanton gas.Comment: 8 pages RevTeX, 5 figures, 2 table

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 quark's 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.Comment: 7 pages, 8 figures; Presented at 27th International Symposium on Lattice Field Theory, Beijing, China, 25 Jul -31 Jul 2009; revision: minor stylistic change

Monopoles and Confining Strings in QCD

We review the recent results in the physics of the magnetic monopoles in gluodynamics and a dual formulation of non-Abelian theories, relevant to the physics of the confinement. It occurs that the dual gluon is a U(1) gauge boson, despite of the fact that usual gluons are non-Abelian. The effective infrared Lagrangian for gluodynamics is suggested which leads to the Casimir scaling of the string tension for quarks in various representations. We also show that the results of the calculations in lattice gauge theories confirm our theoretical predictions.Comment: 36 pp., Latex2e, 9 figures (epsfig). Review based on the plenary talks of M.I.Polikarpov at International Conference "Supersymmetry and Quantum Field Theory", dedicated to the 75th birthday anniversary of Dmitrij Volkov (NSC KIPT, Kharkov, Ukraine 25 - 29 July, 2000) and XVIII CFIF Autumn School "Topology of strongly correlated systems" (Lisbon 8-13 October 2000