arXiv subjects

M. I. Polikarpov

Publications and source records attributed to M. I. Polikarpov.

134 records · Page 8Linked to original sources

arXiv1995

TOPOLOGICAL OBJECTS AND CONFINEMENT ON THE LATTICE

First we discuss various topological objects (monopoles, ``minopoles'' and ``hybrids'') which may be important for the confinement mechanism in various abelian projections. The second topic is the string between quark and antiquark. The standard quantum string with the Nambu-Goto action exists only in D=26. If we start from the field theory, in which the string excitations exist, and change the variables in the path integral to the string variables, then the Jacobian appears. This Jacobian generates the correction to the Nambu-Goto action. For this effective action the conformal anomaly cancels in D=4. Thus we get the quantum string theory in D=4.

hep-lat↗

arXiv1994

"Confinement Mechanism in Various Abelian Projections of $SU(2)$ Lattice Gluodynamics"

We show that the monopole confinement mechanism in lattice gluodynamics is a particular feature of the maximal abelian projection. We give an explicit example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We perform analytical and numerical study of the loop expansion of the Faddeev--Popov determinant for the maximal and the minimal abelian projections, and discuss the fundamental modular region for these projections.

hep-lat↗

arXiv1994

Fractal Dimension of Gauge-fixing Defects

The fractal dimension $D_f$ of sites resisting Landau or maximal Abelian(MA) gauge fixing in lattice $SU(3)$ gluodynamics is defined and computed. In Landau gauge such sites clump into $D_f\sim 1$ clusters in the confining phase. In the finite temperature phase their dimensionality drops to $D_f < 1$, that is, clustering seems to dissipate. In contrast, MA gauge resistant sites fail to exhibit a notable tendency to cluster at any temperature.

hep-lat↗

arXiv1994

Various Abelian Projections of $SU(2)$ Lattice Gluodynamics and Aharonov-Bohm Effect in the Field Theory

We show that in general abelian projection of lattice gluodynamics it is not only monopoles but also strings are present. Both these topological excitations may be responsible for the confinement of color. We illustrate our ideas by some explicit results in the Abelian Higgs model with the Villain action.

hep-lat↗

arXiv1993

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.

hep-lat↗

arXiv1993

Compact QED in Landau Gauge: a lattice gauge fixing case study

We derive different representations of compact QED fixed to Landau gauge by the lattice Faddeev-Popov procedure. Our analysis finds that (A)Nielsen-Olesen vortices arising from the compactness of the gauge-fixing action are {\it quenched\/}, that is, the Faddeev-Popov determinant cancels them out and they do not influence correlation functions such as the photon propagator; (B)Dirac strings are responsible for the nonzero mass pole of the photon propagator. Since in $D=3+1$ the photon mass undergoes a rapid drop to zero at $β_c$, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at $β> β_c$. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at $β\sim β_c$.

hep-lat↗

arXiv1993

String Representation of the Abelian Higgs Theory and Aharonov-Bohm Effect on the Lattice

The partition function of the $4D$ lattice Abelian Higgs theory is represented as the sum over world sheets of Nielsen--Olesen strings. The creation and annihilation operators of the strings are constructed. The topological long--range interaction of the strings and charged particles is shown to exist; it is proportional to the linking number of the string world sheet and particle world trajectory.

hep-lat↗

arXiv1992

Cosmic Strings on the Lattice

We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.

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