140 research outputs found

### 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

### Strings and Aharonov-Bohm Effect in Abelian Higgs Model

We investigate numerically the properties of the Abrikosov-Nielsen-Olesen
strings in 4D abelian Higgs model. The fractal dimension D_f of the vortex
strings was found to be large in the Coulomb phase and it is close to 2 in the
Higgs phase. We also show that the Wilson loop for non-integer charges is
correlated with the linking number of the vortex string world sheets and the
test particle world trajectory. We find that this topological (Aharonov-Bohm)
interaction gives the main contribution to the Wilson loop quantum average for
non-integer test charges in the vicinity of the Coulomb-Higgs phase transition.Comment: 8 pages, LaTeX, 5 EPS-figures, uses epsf.st

### Aharonov--Bohm Effect in 3D Abelian Higgs Theory

We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D
Abelian Higgs Model: the corresponding topological interaction is proportional
to the linking number of the vortex and the particle world trajectories. We
show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of
tested charged particles.Comment: LaTeX, 3 pages, 1 figure, uses epsf.sty; talk presented at
LATTICE96(topology), St. Louis, US

### Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics

't~Hooft's abelian projection of $SU(N)$ gauge theory yields $N$ mutually
constrained, compact abelian fields which are permutationally equivalent. We
formulate the notion of ``species permutation'' symmetry of the $N$ abelian
projection fields and discuss its consequences for cross-species correlators.
We show that at large $N$ cross-species interactions are ${1\over N}$
suppressed relative to same-species interactions. Numerical simulations at
$N=3$ support our symmetry arguments and reveal the existence of inter-species
interactions of size {\cal O\/}\bigl({1\over N-1}\bigr) as analytically
predicted.Comment: 13 pages, 1 postscript figure include

### Various representations of infrared effective lattice QCD

We study various representations of the infrared effective theory of SU(2)
gluodynamics starting from the monopole action derived recently.
We determine the coupling constants in the abelian-Higgs model directly from
lattice QCD and evaluate the type of the QCD vacuum. The string action is
derived using the BKT transformation on the lattice. At the classical level
this action reproduces the physical string tension with a good accuracy.Comment: 3 pages, LaTeX, 2 figures; talk presented at LATTICE9

### Aharonov-Bohm effect, Center Monopoles and Center Vortices in SU(2) Lattice Gluodynamics

SU(2) gluodynamics is investigated numerically and analytically in the
(Indirect) Maximal Center gauge at finite temperature. The center vortices are
shown to be condensed in the confinement phase and dilute in the deconfinement
phase. A new physical object, center monopole, is constructed. We show that the
center monopole condensate is the order parameter of deconfinement phase
transition. The linking of the vortex worldsheets and quark trajectories is
identified with the Aharonov-Bohm interaction in an effective Abelian Higgs
theory. We conclude that the confinement in the Maximal Center gauge can be
explained by a new mechanism called "the real superconductor mechanism".Comment: LATTICE98(confine), 3 pages, LaTeX, 2 eps figures, uses espcrc2.st

### Effective constraint potential in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions for the value
of the Weinberg angle $\theta_W \sim 30^o$, and bare fine structure constant
around $\alpha \sim 1/150$. We consider the value of the scalar self coupling
corresponding to bare Higgs mass around 150 GeV. The effective constraint
potential for the zero momentum scalar field is used in order to investigate
phenomena existing in the vicinity of the phase transition between the physical
Higgs phase and the unphysical symmetric phase of the lattice model. This is
the region of the phase diagram, where the continuum physics is to be
approached. We compare the above mentioned effective potential (calculated in
selected gauges) with the effective potential for the value of the scalar field
at a fixed space - time point. We also calculate the renormalized fine
structure constant using the correlator of Polyakov lines and compare it with
the one - loop perturbative estimate.Comment: LATE

### A fresh look on the flux tube in Abelian-projected SU(2) gluodynamics

We reconsider the properties of the $Q\bar{Q}$ flux tube within
Abelian-projected SU(2) lattice gauge theory in terms of electric field and
monopole current. In the maximal Abelian gauge we assess the influence of the
Gribov copies on the apparent flux-tube profile. For the optimal gauge fixing
we study the independence of the profile on the lattice spacing for $\beta=$
2.3, 2.4, and 2.5115 on a $32^4$ lattice. We decompose the Abelian Wilson loop
into monopole and photon parts and compare the electric and monopole profile
emerging from different sources with the field strength and monopole current
within the dual Ginzburg-Landau theory.Comment: 3 pages, 6 figures, Lattice2002(topology

### Geometry of percolating monopole clusters

We perform detailed measurements of the geometrical characteristics of the
percolating cluster of the magnetic monopole currents in the confining phase of
the lattice SU(2) gluodynamics. The Maximal Abelian projection is used to
define the monopoles. The use of the geometrical language is motivated by
recent observations that the full non-Abelian action associated with the
monopoles corresponds to point-like particles on the currently available
lattices. Scaling behavior of various quantities is observed.Comment: 3 pages, 4 figures, Lattice2002(topology

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