41 research outputs found
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
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
Rigidity and percolation of center vortices
Effective action of center vortices in SU(2) lattice gauge theory is investigated by studying the correlation between the action density on their worldsheets and their geometric properties. It turns out that center vortices are rigid, however, their dynamics is more complicated than that of rigid random surfaces, since some coupling constants have nonstandard scaling dimensions. As a result, the properties of center vortices are almost completely determined by curvature-dependent effects. This, in turn, provides a qualitative explanation of vortex percolation
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
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