Searcharxiv⌕ Search

arXiv subjects

M. I. Polikarpov

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

At least 109 records · Page 6Linked to original sources
arXiv2000

Dirac Strings and Monopoles in the Continuum Limit of SU(2) Lattice Gauge Theory

Magnetic monopoles are known to emerge as leading non-perturbative fluctuations in the lattice version of non-Abelian gauge theories in some gauges. In terms of the Dirac quantization condition, these monopoles have magnetic charge |Q_M|=2. Also, magnetic monopoles with |Q_M|=1 can be introduced on the lattice via the 't Hooft loop operator. We consider the |Q_M|=1,2 monopoles in the continuum limit of the lattice gauge theories. To substitute for the Dirac strings which cost no action on the lattice, we allow for singular gauge potentials which are absent in the standard continuum version. Once the Dirac strings are allowed, it turns possible to find a solution with zero action for a monopole--antimonopole pair. This implies equivalence of the standard and modified continuum versions in perturbation theory. To imitate the nonperturbative vacuum, we introduce then a nonsingular background. The modified continuum version of the gluodynamics allows in this case for monopoles with finite non-vanishing action. Using similar techniques, we construct the 't Hooft loop operator in the continuum and predict its behavior at small and large distances both at zero and high temperatures.

hep-th↗
arXiv2000

Confinement and short distance physics

We consider non-perturbative effects at short distances in theories with confinement. The analysis is straightforward within the Abelian models in which the confinement arises on classical level. In all cases considered (compact U(1) in 3D and 4D, dual Abelian Higgs model) there are non-perturbative contributions associated with short distances which are due to topological defects. In QCD case, both classical and quantum effects determine the role of the topological defects and the theoretical analysis has not been completed so far. Generically, the topological defects would result in 1/Q^2 corrections going beyond the standard Operator Product Expansion. We review existing data on the power corrections and find that the data favor existence of the novel corrections, at least at the mass scale of (1-2) GeV. We indicate crucial experiments which could further clarify the situation on the phenomenological side.

hep-ph↗
arXiv2000

P-vortices, nexuses and effects of gauge copies

We perform the careful study of the gauge copies problem for the direct center projection in SU(2) lattice gauge theory. Our results indicate that this gauge is not appropriate for the investigation of the center vortices. We also show that the point-like objects, nexuses, are important for the confinement dynamics.

hep-lat↗
arXiv1999

Short Strings and New Physics Perspectives in QCD

Within the (dual) Abelian Higgs model, confining strings do not disappear at small distances but rather become short strings. In compact 3D electrodynamics, as we argue here, the confining strings are also manifested at small distances in unusual power corrections, disobeying the standard rules of the Operator Product expansion. In the most interesting case of QCD, there is yet no derivation of short strings and we turn to phenomenology to find evidence pro or contra their existence. The short strings in QCD lead to non-standard power corrections. A tentative conclusion of the analysis of existing data, both in numerical simulations and in real experiments, is that the novel power corrections are present, at least at the mass scale of 1-2 GeV.

hep-lat↗
arXiv1999

The lattice SU(2) confining string as an Abrikosov vortex

Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.

hep-lat↗
arXiv1999

Short Strings and Gluon Propagator in the Infrared Region

We discuss how infrared region influence on short distance physics via new object, called ``short string''. This object exists in confining theories and violates the operator product expansion. Most analytical results are obtained for the dual Abelian Higgs theory, while phenomenological arguments are given for QCD.

hep-lat↗
arXiv1999

Physics of the Power Corrections in QCD

We review the physics of the power corrections to the parton model. In the first part, we consider the power corrections which characterize the infrared sensitivity of Feynman graphs when the contribution of short distances dominates. The second part is devoted to the hypothetical power corrections associated with nonperturbative effects at small distances.

hep-ph↗
arXiv1999

Power Corrections from Small Distances

We review recent speculations on power like corrections in QCD which go beyond the standard Operator Product Expansion. Both the theoretical picture underlying these corrections and phenomenological manifestations are discussed in some detail.

hep-ph↗
arXiv1999

Short Strings in Abelian Higgs Model

We consider the monopole-antimonopole static potential in the confining phase of the Abelian Higgs model and in particular the corrections to the Coulomb-like potential at small distances r. By minimizing numerically the classical energy functional we observe a linear in r, stringy correction even at distances much smaller than the apparent physical scales. We argue that this term is a manifestation of the condition that the monopoles are connected by a mathematically thin line along which the scalar field vanishes. These short strings modify the operator product expansion as well. Implications for QCD are discussed.

hep-th↗
arXiv1999

Infrared Behaviour of the Gauge Boson Propagator in a Confining Theory

We study the gauge boson propagator in the dual Abelian Higgs theory which confines electric charges. The confinement is due to dual Abrikosov-Nielsen-Olesen strings. We show that the infrared double pole 1/(p^2)^2 in the propagator is absent due to the confinement phenomenon. Instead, specific angular singularities signal the eventual set in of the confinement. These angular singularities are a manifestation of the confining strings.

hep-ph↗
arXiv1998

Effective Monopole Potential for SU(2) Lattice Gluodynamics in Spatial Maximal Abelian Gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We show numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement: the abelian condensate vanishes in the deconfinement phase and is not zero in the confinement phase.

hep-lat↗
arXiv1998

Abelian Dyons in the Maximal Abelian Projection of SU(2) Gluodynamics

Correlations of the topological charge Q, the electric current J^e and the magnetic current J^m in SU(2) lattice gauge theory in the Maximal Abelian projection are investigated. It occurs that the correlator < > is nonzero for a wide range of values of the bare charge. It is shown that: (i) the abelian monopoles in the Maximal Abelian projection are dyons which carry fluctuating electric charge; (ii) the sign of the electric charge e(x) coincides with that of the product of the monopole charge m(x) and the topological charge density Q(x).

hep-lat↗
arXiv1998

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".

hep-lat↗
arXiv1998

Monopole-antimonopole interaction in Abelian Higgs model

We consider interaction of a probe monopole-antimonopole pair in the vacuum of the Abelian Higgs model. For simplicity, the mass of the Higgs particle is assumed to be much larger than the mass of the photon (London limit). In case of a massive photon the straightforward application of the Zwanziger formalism to accommodate both magnetic and electric charges is known to result in gauge dependence and infrared instabilities. We argue that the use of the string representation of the Abelian Higgs model allows to ameliorate both difficulties. In particular, we arrive at a well defined expression for the potential energy of the static monopole sources. We argue that the monopole-antimonopole interaction cannot be described by a massive photon exchange with a definite propagator having simple analytical properties.

hep-th↗
arXiv1998

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.

hep-lat↗
arXiv1998

Dyon Condensation and Aharonov-Bohm Effect

We derive the string representation of the Abelian Higgs theory in which dyons are condensed. It occurs that in such representation the topological interaction exists in the expectation value of the Wilson loop. Due to this interaction the dynamics of the string spanned on the Wilson loop is non-trivial.

hep-th↗