arXiv subjects

V. I. Zakharov

Publications and source records attributed to V. I. Zakharov.

At least 73 records · Page 4Linked to original sources

arXiv2006

From confining fields on the lattice to higher dimensions in the continuum

We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional defects, that is monopoles, center vortices, topological defects. There is certain resemblance to dual strings, domain walls, introduced in large-N Yang-Mills theories.

hep-ph↗

arXiv2006

Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory

We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also measure the density of low-lying eigenmodes, and find a possible connection to multi-critical matrix models of order m=1.

hep-lat↗

arXiv2006

Matter of resolution: from quasiclassics to fine tuning

Recently, there appeared results of lattice measurements in Yang-Mills theories which indicate non-trivial dependences on the lattice spacing of many observables. In particular, volume occupied by fermionic zero modes shrinks to zero in the continuum limit. These results are in apparent disagreement with quasiclassical models which assume that all the non-perturbative effects develop on the scale of $Λ_{QCD}$. We emphasize that this kind of contradictions might be superficial since the results in point depend in fact on the measurements procedure. The lattice simulations correspond to measurements with high resolution while the quasiclassical picture assumes poor resolution. We will argue that the general trend is that what looks quasiclassical in measurements with poor resolution becomes fine tuned in measurements with fine resolution. The main emphasis is on the topological fermionic modes and we argue that shrinking of the volume occupied by the modes could have been predicted theoretically.

hep-ph↗

arXiv2005

On topological properties of vacuum defects in lattice Yang-Mills theories

We study correlations between low-lying modes of the overlap Dirac operator and vacuum defects, center vortices and three-dimensional volumes, in lattice SU(2) gluodynamics. The low-lying modes are apparently sensitive to topological properties of the underlying gluon field configurations while the vacuum defects are crucial for the confinement. We find distinct positive correlation in both cases. In case of vortices the correlation is stronger.

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arXiv2005

Localization of Low Lying Eigenmodes for Chirally Symmetric Dirac Operator

We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. The situation changes drastically when we study "vortex removed" configurations.

hep-lat↗

arXiv2005

Eigenmodes of covariant Laplacian in SU(2) Yang-Mills vacuum: higher representations

The study of lowest eigenmodes of the covariant Laplacian in fundamental representation of the gauge group revealed their specific localization properties. These may bear information on confinement of fundamental scalar particles in SU(2) Yang-Mills vacuum. It was expected that scalar particle eigenmodes in other representations would be localized in different physical volumes. However simulations show strikingly different results for the adjoint and higher (J=3/2) representations. Apart from much higher extent of localization, we find evidence of different scaling behavior of localized eigenmodes.

hep-lat↗

arXiv2005

Geometry of three dimensional vacuum domains in four dimensional SU(2) gluodynamics

We review briefly recent results of lattice simulations on 3d domains in the vacuum state of SU(2) gluodynamics. The defects are defined as unification of all the negative links in central projection under condition that the total number of negative links is minimized. In the continuum limit, negative links correspond, generally speaking to singular fields. The data indicate that total volume of the defects scales in physical units. We consider also correlator of negative links. The correlator scales in physical units as well, within the error bars. A new observation reported here is a strong anisotropy of the correlator.

hep-lat↗

arXiv2005

Towards SU(2) invariant formulation of the monopole confinement mechanism

The type of the vacuum is studied numerically in the maximally Abelian (MA) gauge and in the Landau (LA) gauge of SU(2) gluodynamics. The type of the vacuum is determined by a ratio between the dual coherence and the dual penetration lengths. The dual penetration length is determined from correlations between Wilson loops and electric fields in both gauges. The dual coherence length is found from correlations between Wilson loops and dimension-2 operators both in the MA and the LA gauges. This determination of the coherence length is supported by theoretical and numerical observation that the dimension-2 gluon operators in the studied gauges have a strong correlation with the monopole current determined in the MA gauge. We find numerically that the dual penetration lengths and the dual coherence lengths in the LA and the MA gauges are almost the same. Therefore we conclude, that in both gauges the type of the vacuum in the confinement phase is near to the border between the type 1 and the type 2 dual superconductors.

hep-lat↗

arXiv2005

Localized eigenmodes of the covariant lattice Laplacian

We study numerically the eigenmode spectrum of the covariant lattice Laplacian, in the fundamental SU(2) color group representation. It is found that eigenmodes at the lower and upper ends of the spectrum are localized, and that the localization volume scales. In contrast, the eigenmodes of the lattice Faddeev-Popov operator are all extended rather than localized (as required for confinement) despite the similarity of the kinetic and Faddeev-Popov operators.

hep-lat↗

arXiv2005

From confining fields back to power corrections

We overview the issue of the power corrections to the parton model, mostly within the context of QCD sum rules. There are a few sources of the power corrections responsible for various qualitative effects. The basic idea that the power corrections are related to confining fields seems to be realized in case of $1/Q^2$ corrections which are dual to high orders of perturbation theory. The evidence comes from lattice studies of the confinement which allowed to identify the confining field configurations as monopoles and vortices. We comment also on the role of the condensate of dimension two, $<(A_μ^a)^2>_{min}$.

hep-ph↗

arXiv2005

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.

hep-lat↗

arXiv2005

Evidence for fine tuning of fermionic modes in lattice gluodynamics

We consider properties of zero and near-zero fermionic modes in lattice gluodynamics. The modes are known to be sensitive to the topology of the underlying gluonic fields in the quantum vacuum state of the gluodynamics. We find evidence that these modes are fine tuned, that is exhibit sensitivity to both physical (one can say, hadronic) scale and to the ultraviolet cutoff. Namely, the density of the states is in physical units while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. We discuss briefly possible theoretical implications and also include some general, review-type remarks.

hep-lat↗

arXiv2005

Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum

As a probe of the Yang-Mills vacuum, we study numerically the eigenmode spectrum of the covariant lattice Laplacian operator. We find that the eigenmodes at the low and high ends of the spectrum are localized in finite regions whose volume is insensitive to the lattice volume. We also find that the vacuum is seen very differently by localized modes of the covariant Laplacian in different representations of the gauge group. In the fundamental representation, the data suggests that the localization volume is finite in physical units set by the string tension, and localization disappears when center vortices are removed. In the adjoint and j=3/2 representations the low and high-lying modes are far more localized, and the localization volume appears to scale to zero, in physical units, in the continuum limit. The adjoint Laplacian is insensitive to vortex removal, but we find that exponential localization is absent for adjoint eigenmodes in the Higgs phase of a gauge-Higgs theory. Localization is also absent in the spectrum of the Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement scenarios.

hep-lat↗

arXiv2005

Dual string from lattice Yang-Mills theory

We review properties of lower-dimension vacuum defects observed in lattice simulations of SU(2) Yang-Mills theories. One- and two-dimensional defects are associated with ultraviolet divergent action. The action is the same divergent as in perturbation theory but the fluctuations extend over submanifolds of the whole 4d space. The action is self tuned to a divergent entropy and the 2d defects can be thought of as dual strings populated with particles. The newly emerging 3d defects are closely related to the confinement mechanism. Namely, there is a kind of holography so that information on the confinement is encoded in a 3d submanifold. We introduce an SU(2) invariant classification scheme which allows for a unified description of d=1,2,3 defects. The scheme fits known data and predicts that the 3d defects are related to chiral symmetry breaking. Relation to stochastic vacuum model is briefly discussed as well.

hep-ph↗

arXiv2004

Lower-dimension vacuum defects in lattice Yang-Mills theory

We overview lattice data on d=1,2,3 vacuum defects in four-dimensional gluodynamics. In all the cases defects have total volume which scales in physical units (with zero fractal dimension). In case of d=1,2 the defects are distinguished by ultraviolet divergent non-Abelian action as well. This sensitivity to the ultraviolet scale allows to derive from the continuum theory strong constraints on the properties of the defects. The constraints turn to be satisfied by the lattice data. In the SU(2) case we introduce a classification scheme of the defects which allows to (at least) visualize the defect properties in a simple and unified way. Not-yet-checked relation of the defects to the spontaneous chiral symmetry breaking is suggested by the scheme.

hep-ph↗

arXiv2004

Three dimensional vacuum domains in four dimensional SU(2) gluodynamics

Performing lattice simulations of the four dimensional SU(2)gluodynamics we find evidence for existence of three-dimensional domains whose total volume scales in physical units. Technically, the domains are defined in terms of the minimal density of negative links in Z(2) projection of gauge fields. The volume can be viewed also as the minimal volume bound by the center vortices. We argue that the three-dimensional domains are closely related to confinement.

hep-lat↗

arXiv2004

Properties of P-vortex and monopole clusters in lattice SU(2) gauge theory

We study the action and geometry of P-vortices, discriminating between the percolating and finite clusters. We also discuss the interrelation of the monopoles and P-vortices. To define P-vortices we use both the direct maximal center projection and indirect maximal center projection. We find, in particular, that the action density of the P-vortices in short clusters is substantially higher than in the percolating cluster. The surface of the percolating cluster appears random at short distances, with action density depending on the shape.

hep-lat↗

arXiv2004

A novel probe of the vacuum of the lattice gluodynamics

We introduce a notion of minimal number of negative links on the lattice for a given original configuration of SU(2) fields. Negative links correspond to a large potential, not necessarily large action. The idea is that the minimal number of negative links is a gauge invariant notion. To check this hypothesis we measure correlator of two negative links, averaged over all the directions, as function of the distance between the links. The inverse correlation length coincides within the error bars with the lightest glueball mass.

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