25 research outputs found
Random walks of Wilson loops in the screening regime
Dynamics of Wilson loops in pure Yang-Mills theories is analyzed in terms of
random walks of the holonomies of the gauge field on the gauge group manifold.
It is shown that such random walks should necessarily be free. The distribution
of steps of these random walks is related to the spectrum of string tensions of
the theory and to certain cumulants of Yang-Mills curvature tensor. It turns
out that when colour charges are completely screened, the holonomies of the
gauge field can change only by the elements of the group center, which
indicates that in the screening regime confinement persists due to thin center
vortices. Thick center vortices are also considered and the emergence of such
stepwise changes in the limits of infinitely thin vortices and infinitely large
loops is demonstrated.Comment: Major revision of the previous version, to appear in Nucl. Phys. B
(10 pages RevTeX, 3 figures
Entanglement entropy in gauge theories and the holographic principle for electric strings
We consider quantum entanglement between gauge fields in some region of space
A and its complement B. It is argued that the Hilbert space of physical states
of gauge theories cannot be decomposed into a direct product of Hilbert spaces
of states localized in A and B. The reason is that elementary excitations in
gauge theories - electric strings - are associated with closed loops rather
than points in space, and there are closed loops which belong both to A and B.
Direct product structure and hence the reduction procedure with respect to the
fields in B can only be defined if the Hilbert space of physical states is
extended by including the states of electric strings which can open on the
boundary of A. The positions of string endpoints on this boundary are the
additional degrees of freedom which also contribute to the entanglement
entropy. We explicitly demonstrate this for the three-dimensional Z2 lattice
gauge theory both numerically and using a simple trial ground state wave
function. The entanglement entropy appears to be saturated almost completely by
the entropy of string endpoints, thus reminding of a ``holographic principle''
in quantum gravity and AdS/CFT correspondence.Comment: 6 pages RevTeX, 5 figure
Center vortices as rigid strings
It is shown that the action associated with center vortices in SU(2) lattice
gauge theory is strongly correlated with extrinsic and internal curvatures of
the vortex surface and that this correlation persists in the continuum limit.
Thus a good approximation for the effective vortex action is the action of
rigid strings, which can reproduce some of the observed geometric properties of
center vortices. It is conjectured that rigidity may be induced by some fields
localized on vortices, and a model-independent test of localization is
performed. Monopoles detected in the Abelian projection are discussed as
natural candidates for such two-dimensional fields.Comment: 7 pages, 8 figures, RevTeX
Chiral Magnetic Effect on the Lattice
We review recent progress on the lattice simulations of the chiral magnetic
effect. There are two different approaches to analyze the chiral magnetic
effect on the lattice. In one approach, the charge density distribution or the
current fluctuation is measured under a topological background of the gluon
field. In the other approach, the topological effect is mimicked by the chiral
chemical potential, and the induced current is directly measured. Both
approaches are now developing toward the exact analysis of the chiral magnetic
effect.Comment: to appear in Lect. Notes Phys. "Strongly interacting matter in
magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A.
Schmitt, H.-U. Ye
Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field
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
\sqrt{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.Comment: 6 pages, Elsevier article style, 5 figures; revision: references and
discussions added, published versio
Chiral magnetization of non-Abelian vacuum: a lattice study
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.Comment: 8 pages, 3 figures, uses elsarticle style; revision: factorization
checked numerically, references added, published versio
Lattice QCD Simulations in External Background Fields
We discuss recent results and future prospects regarding the investigation,
by lattice simulations, of the non-perturbative properties of QCD and of its
phase diagram in presence of magnetic or chromomagnetic background fields.
After a brief introduction to the formulation of lattice QCD in presence of
external fields, we focus on studies regarding the effects of external fields
on chiral symmetry breaking, on its restoration at finite temperature and on
deconfinement. We conclude with a few comments regarding the effects of
electromagnetic background fields on gluodynamics.Comment: 31 pages, 10 figures, minor changes and references added. To appear
in Lect. Notes Phys. "Strongly interacting matter in magnetic fields"
(Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye
Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory
We argue that in the infrared regime of continuum Yang-Mills theory, the
possibility of a mass gap in the charged sector is closely associated with the
center vortex sector.
The analysis of the possible consequences of the ensembles of defects is done
by showing that the description of center vortices and monopoles is naturally
unified by means of a careful treatment of Cho decomposition.
If on the one hand confinement is usually associated with monopole
condensation in a compact abelian model, in this scenario, the previous
decoupling of the off-diagonal degrees of freedom, for the abelian model
dominate at large distances, can be understood as induced by a phase where
center vortices become thick objects.
Other important scenarios for correlated monopoles and center vortices,
observed in lattice simulations, are also accomodated in our general
formulation.Comment: 36 pages, improved version containing a more general discussio
The Chiral Magnetic Effect and Axial Anomalies
We give an elementary derivation of the chiral magnetic effect based on a
strong magnetic field lowest-Landau-level projection in conjunction with the
well-known axial anomalies in two- and four-dimensional space-time. The
argument is general, based on a Schur decomposition of the Dirac operator. In
the dimensionally reduced theory, the chiral magnetic effect is directly
related to the relativistic form of the Peierls instability, leading to a
spiral form of the condensate, the chiral magnetic spiral. We then discuss the
competition between spin projection, due to a strong magnetic field, and
chirality projection, due to an instanton, for light fermions in QCD and QED.
The resulting asymmetric distortion of the zero modes and near-zero modes is
another aspect of the chiral magnetic effect.Comment: 33 pages, 5 figures, to appear in Lect. Notes Phys. "Strongly
interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K.
Landsteiner, A. Schmitt, H.-U. Ye
Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
We study a gauge invariant order parameter for deconfinement and the chiral
condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the
deconfinement phase transition using the Landau gauge quark and gluon
propagators. We determine the gluon propagator from lattice calculations and
the quark propagator from its Dyson-Schwinger equation, using the gluon
propagator as input. The critical temperature and a deconfinement order
parameter are extracted from the gluon propagator and from the dependency of
the quark propagator on the temporal boundary conditions. The chiral transition
is determined using the quark condensate as order parameter. We investigate
whether and how a difference in the chiral and deconfinement transition between
SU(2) and SU(3) is manifest.Comment: 15 pages, 9 figures. For clarification one paragraph and two
references added in the introduction and two sentences at the end of the
first and last paragraph of the summary. Appeared in EPJ