Abelian representation for nonabelian Wilson loops and the Non - Abelian Stokes theorem on the lattice

We derive the Abelian - like expression for the lattice SU(N) Wilson loop in arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without selfintersections) that has been obtained by Diakonov and Petrov appears to be a continuum limit of this expression. We also obtain the lattice variant of a non - Abelian Stokes theorem and present the explicit expression for the matrix $\cal H$ used in the Diakonov - Petrov approach.Comment: revtex, 10 pages, ITEP-LAT/2002-3

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

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

Monopoles in the Abelian Projection of Gluodynamics

We discuss some properties of the abelian monopoles in compact U(1) gauge theory and in the SU(2) gluodynamics both on the lattice and in the continuum.Comment: 13 pages, 7 eps figures, LaTeX using PTPTEX.sty (included); Lectures given by M.I.Polikarpov at the 1997 Yukawa International Seminar on "Non-perturbative QCD - Structure of QCD Vacuum -" (YKIS'97), 2-12 December, 1997, Yukawa Institute for Theoretical Physics, Kyoto, Japa