arXiv subjects

V. I. Zakharov

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

At least 109 records · Page 6Linked to original sources

arXiv2001

Hints on the power corrections from current correlators in x-space

We consider an interpretation of the recent lattice data on the current-current correlators in the x-space. The data indicate rather striking difference between (axial)vector and (pseudo)scalar channels which goes beyond the predictions of the standard non-perturbative models. We argue that if the difference is to be explained by power corrections, there is a unique choice of the form of the correction. We discuss the emerging picture of the power corrections.

hep-ph↗

arXiv2001

Heavy monopole potential in gluodynamics

We discuss predictions for the interaction energy of the fundamental monopoles in gluodynamics introduced via the 't Hooft loop. At short distances, the heavy monopole potential is calculable from first principles. At larger distances, we apply the Abelian dominance models. We discuss the measurements which would be crucial to distinguish between various models. Non-zero temperatures are also considered. Our predictions are in qualitative agreement with the existing lattice data. We discuss further measurements which would be crucial to check the model.

hep-lat↗

arXiv2001

The Berry Phase and Monopoles in Gluodynamics

We introduce a gauge invariant definition of a monopole on the lattice. The construction is based on the observation that for each Wilson loop there exists an extra U(1) group which leaves the loop invariant. Since the lattice formulation utilizes the language of Wilson loops, the definition of the monopole charge in terms of this plaquette dependent U(1) is gauge invariant. The explicit construction of gauge invariant monopoles is presented both in continuum and on the lattice.

hep-lat↗

arXiv2001

Monopoles and Confining Strings in QCD

We review the recent results in the physics of the magnetic monopoles in gluodynamics and a dual formulation of non-Abelian theories, relevant to the physics of the confinement. It occurs that the dual gluon is a U(1) gauge boson, despite of the fact that usual gluons are non-Abelian. The effective infrared Lagrangian for gluodynamics is suggested which leads to the Casimir scaling of the string tension for quarks in various representations. We also show that the results of the calculations in lattice gauge theories confirm our theoretical predictions.

hep-lat↗

arXiv2000

On the heavy monopole potential in gluodynamics

hep-ph↗

arXiv2000

Towards Abelian-like formulation of the dual gluodynamics

We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Q|=1 monopoles introduced via the `t Hooft loop can be considered consistently. We show that at short distances the external monopoles interact as pure Abelian objects. This result can be reproduced by a Zwanziger-type Lagrangian with an Abelian dual gluon. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles |Q|=2 can be considered as point-like as well. Assuming the monopole condensation we arrive at a model which is reminiscent in some respect of the Abelian Higgs model but, unlike the latter leaves space for the Casimir scaling.

hep-th↗

arXiv2000

On the Emerging Phenomenology of <(A_μ)^2>

We discuss phenomenology of the vacuum condensate <(A_μ)^2> in pure gauge theories, where A_μis the gauge potential. Both Abelian and non-Abelian cases are considered. In case of the compact U(1) the non-perturbative part of the condensate <(A_μ)^2> is saturated by monopoles. In the non-Abelian case, a two-component picture for the condensate is presented according to which finite values of order Λ_{QCD}^2 are associated both with large and short distances. We obtain a lower bound on the <(A_μ)^2> by considering its change at the phase transition. Numerically, it produces an estimate similar to other measurements. Possible physical manifestations of the condensate are discussed.

hep-ph↗

arXiv2000

On the Significance of the Quantity "A Squared"

We consider the gauge potential A and argue that the minimum value of the volume integral of A squared (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and non-compact ``photodynamics'' shows a jump in this quantity at the phase transition, supporting this idea.

hep-ph↗

arXiv2000

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. In this review, written for a memorial volume dedicated to the memory of Academician A.B. Migdal, we emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.

hep-th↗

arXiv2000

The Berry Phase and Monopoles in Non-Abelian Gauge Theories

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorenz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

hep-th↗

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↗

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

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

Gluon Condensate and Beyond

We review briefly and in retrospect the development which brought about the QCD sum rules based on introduction of the gluon condensate (M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov (1978)).

hep-ph↗