arXiv subjects

Dmitri Antonov

Publications and source records attributed to Dmitri Antonov.

At least 19 recordsLinked to original sources

arXiv2012

Quark condensate for various heavy flavors

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64%-decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang-Mills fields.

hep-ph↗

arXiv2012

Triviality of the Aharonov-Bohm interaction in a spatially confining vacuum

This paper explores long-range interactions between magnetically-charged excitations of the vacuum of the dual Landau-Ginzburg theory (DLGT) and the dual Abrikosov vortices present in the same vacuum. We show that, in the London limit of DLGT, the corresponding Aharonov-Bohm-type interactions possess such a coupling that the interactions reduce to a trivial factor of e^{2πi (integer)}. The same analysis is done in the SU(N_c)-inspired [U(1)]^{N_c-1}-invariant DLGT, as well as in DLGT extended by a Chern-Simons term. It is furthermore explicitly shown that the Chern-Simons term leads to the appearance of knotted dual Abrikosov vortices.

hep-th↗

arXiv2012

Shear viscosity of a nonperturbative gluon plasma

Shear viscosity is evaluated within a model of the gluon plasma, which is based entirely on the stochastic nonperturbative fields. We consider two types of excitations of such fields, which are characterized by the thermal correlation lengths ~ 1/(g^2 T) and ~ 1/(g^4 T), where "g" is the finite-temperature Yang-Mills coupling. Excitations of the first type correspond to the genuine nonperturbative stochastic Yang-Mills fields, while excitations of the second type mimic the known result for the shear viscosity of the perturbative Yang-Mills plasma. We show that the excitations of the first type produce only an O(g^{10})-correction to this result. Furthermore, a possible interference between excitations of these two types yields a somewhat larger, O(g^7), correction to the leading perturbative Yang-Mills result. Our analysis is based on the Fourier transformed Euclidean Kubo formula, which represents an integral equation for the shear spectral density. This equation is solved by seeking the spectral density in the form of the Lorentzian Ansätze, whose widths are defined by the two thermal correlation lengths and by their mean value, which corresponds to the said interference between the two types of excitations. Thus, within one and the same formalism, we reproduce the known result for the shear viscosity of the perturbative Yang-Mills plasma, and account for possible nonperturbative corrections to it.

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arXiv2010

Exploring correlations in the stochastic Yang-Mills vacuum

The correlation lengths of nonperturbative-nonconfining and confining stochastic background Yang-Mills fields are obtained by means of a direct analytic path-integral evaluation of the Green functions of the so-called one- and two-gluon gluelumps. Numerically, these lengths turn out to be in a good agreement with those known from the earlier, Hamiltonian, treatment of such Green functions. It is also demonstrated that the correlation function of nonperturbative-nonconfining fields decreases with the deviation of the path in this correlation function from the straight-line one.

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arXiv2010

Contributions of stochastic background fields to the shear and bulk viscosities of the gluon plasma

The contributions of confining as well as nonconfining nonperturbative self-interactions of stochastic background fields to the shear and bulk viscosities of the gluon plasma in SU(3) Yang-Mills theory are calculated. The nonconfining self-interactions change (specifically, diminish) the values of the shear and bulk viscosities by 15%, that is close to the 17% which the strength of the nonconfining self-interactions amounts of the full strength of nonperturbative self-interactions. The ratios to the entropy density of the obtained nonperturbative contributions to the shear and bulk viscosities are compared with the results of perturbation theory and the predictions of {\cal N}=4 SYM.

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arXiv2009

Shear viscosity of the gluon plasma in the stochastic-vacuum approach

Shear viscosity of the gluon plasma in SU(3) YM theory is calculated nonperturbatively, within the stochastic vacuum model. The result for the ratio of the shear viscosity to the entropy density, proportional to the squared chromo-magnetic gluon condensate and the fifth power of the correlation length of the chromo-magnetic vacuum, falls off with the increase of temperature. At temperatures larger than the deconfinement critical temperature by a factor of 2, this fall-off is determined by the sixth power of the temperature-dependent strong-coupling constant and yields an asymptotic approach to the conjectured lower bound of 1/(4π), achievable in {\cal N}=4 SYM theory. As a by-product of the calculation, we find a particular form of the two-point correlation function of gluonic field strengths, which is the only one consistent with the Lorentzian shape of the shear-viscosity spectral function.

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arXiv2005

Calculating the gauge-invariant two-point correlation function of gluonic field strengths

The two-point gauge-invariant correlation function of gluonic field strengths, which is the main input in the stochastic vacuum model, is derived by using its relation to the Green functions of one- and two-gluon gluelumps. These Green functions are found by evaluating the path integrals of one and two gluons confined in the field of an infinitely heavy adjoint source. This allows one to obtain also the terms in the exponential asymptotics of the two-point correlation function, which are produced by fluctuations of the gluons around their mean separation from the source. The pre-exponents are derived as well, demonstrating some novel dependences on the distance.

hep-ph↗

arXiv2005

Mixed heavy-quark-gluon condensate in the stochastic vacuum model and dual superconductor

The world-line formalism is used for the evaluation of the mixed heavy-quark-gluon condensate in two models of QCD - the stochastic vacuum model and the dual superconductor one. Calculations are performed for an arbitrary dimensionality of space-time $d\ge 2$. While in the stochastic vacuum model, the condensate is UV finite up to $d=8$, in the dual superconductor model it is UV divergent at any $d\ge 2$. A regularization of this divergence is proposed, which makes quantitative the condition of the type-II dual superconductor. The obtained results are generalized to the case of finite temperatures. Corrections to the both, mixed and standard, heavy-quark condensates, which appear due to the variation of the gauge field at the scale of the vacuum correlation length, are evaluated within the stochastic vacuum model. These corrections diminish the absolute values of the condensates, as well as the ratio of the mixed condensate to the standard one.

hep-ph↗

arXiv2005

Influence of matter fields on the (de-)confining properties of the 3d Georgi-Glashow model

The influence of various matter fields on the confining and finite-temperature properties of the (2+1)d Georgi-Glashow model is explored. At zero temperature, these fields are W-bosons, which play the role of heavy nodes, through which the quark-antiquark string passes. This fact is shown to increase by a factor $4\sqrt{2}$ the absolute value of the coefficient at the 1/R-term in the large-distance potential with respect to that of the Nambu-Goto string in 3d. The string tension also acquires a positive correction, which is, however, exponentially small. At finite temperature, the matter fields of interest are massless fundamental quarks, which diminish the deconfinement critical temperature by way of an additional attraction of a monopole and an antimonopole inside their molecules through the quark zero modes. It is demonstrated that, outside the BPS-limit, when the number of massless flavors is 4 or larger, the deconfinement phase transition occurs already at the temperatures of the order of the temperature of dimensional reduction. In the BPS limit, this critical number of flavors is 3. Since the temperature of dimensional reduction is exponenetially small and since monopoles are instantons in (2+1)d, these numbers can be compared with the one in the instanton-liquid model of 4d QCD, at which the chiral phase transition occurs at a vanishingly small temperature. The latter number is known to be of the order of 5, so that the results of the two models are quite close to each other.

hep-th↗

arXiv2004

Heavy-quark condensate at zero and finite temperatures for various forms of the short-distance potential

With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, which takes place in the stochastic vacuum model, the standard QCD-sum-rules result is reproduced. In the other case, the condensate turns out to be UV-finite only in less than four dimensions. This fact excludes a possibility to have, in four dimensions, the linear term in the potential, as well as short strings, at the distances smaller than the vacuum correlation length. The use of the world-line formalism enables one to generalize further both results for the condensate to the case of finite temperatures. A generalization of the QCD-sum-rules result to the case of an arbitrary number of space-time dimensions is also obtained and turns out to be UV-finite, provided this number is smaller than six.

hep-ph↗

arXiv2004

k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

The k-string tensions are explored in the 4-d $[U(1)]^{N-1}$-invariant dual Abelian-Higgs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N-ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N-ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the non-diluteness of the monopole plasma in the 3-d SU(N) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.

hep-th↗

arXiv2004

Confinement in the Abelian-Higgs-type theories: string picture and field correlators

Field correlators and the string representation are used as two complementary approaches for the description of confinement in the SU(N)-inspired dual Abelian-Higgs-type model. In the London limit of the simplest, SU(2)-inspired, model, bilocal electric field-strength correlators have been derived with accounting for the contributions to these averages produced by closed dual strings. The Debye screening in the plasma of such strings yields a novel long-range interaction between points lying on the contour of the Wilson loop. This interaction generates a Luescher-type term, even when one restrics oneself to the minimal surface, as it is usually done in the bilocal approximation to the stochastic vacuum model. Beyond the London limit, it has been shown that a modified interaction appears, which becomes reduced to the standard Yukawa one in the London limit. Finally, a string representation of the SU(N)-inspired model with the theta-term, in the London limit, can be constructed.

hep-th↗

arXiv2003

k-string tensions in the 3-d SU(N) Georgi-Glashow model

The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k is of the order of N, the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same k-dependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N-dependence. Finally, we consider the possible implications of our analysis for the SU(N) analogue of compact QED in four dimensions.

hep-th↗

arXiv2003

SU(N) fundamental and adjoint confining strings

String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. Using for concreteness the three-dimensional fundamental case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when deduced from the mean magnetic field inside a flat contour (the derivation of this field is also presented). Moreover, the obtained theory enables one to find also the coupling constants of terms in the expansion of the nonlocal string effective action, which are higher in the derivatives than the Nambu-Goto term (some of these terms vanish at the flat surface). In the four-dimensional case with the theta-term, the critical values of the theta-parameter, at which the problem of crumpling of large world sheets might be solved, are found in both the fundamental case and in the large-N limit of the adjoint case. These values are only accessible provided the electric coupling constant is larger than a certain value, in accordance with the known fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.

hep-th↗

arXiv2003

Heavy-quark condensate at zero- and nonzero temperatures for various forms of the short-distance potential

With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, the standard QCD-sum-rules result is reproduced, while the latter result is a novel one. Explicitly, it is UV-finite only in less than four dimensions. This fact excludes a possibility to have, in four dimensions, very short strings (whose length has the scale of the lattice spacing), and consequently the short-range linear potential (if it exists) cannot violate the OPE. In any number of dimensions, the obtained novel expression for the quark condensate depends on the string tension at short distances, rather than on the gluon condensate, and grows linearly with the number of colors in the same way as the standard QCD-sum-rules expression. The use of the world-line formalism enables one to generalize further both results to the case of finite temperatures. A generalization of the QCD-sum-rules expression to the case of an arbitrary number of space-time dimensions is also obtained and is shown to be UV-finite, provided this number is smaller than six.

hep-ph↗

arXiv2002

Exploring quark-gluon plasma on the loop space

Langevin equation describing soft modes in the quark-gluon plasma is reformulated on the loop space. The Cauchy problem for the resulting loop equation is solved for the case when the nonvanishing components of the gauge potential correspond to the Cartan generators of the SU(N)-group and are proportional to a constant unit vector in the Cartan subalgebra. The regularized form of the loop equation with an arbitrary gauge potential is found, and perturbation theory in powers of the 't Hooft coupling is discussed.

hep-th↗

arXiv2002

Finite-temperature behavior of the (2+1)D Georgi-Glashow model with and without quarks

(2+1)-dimensional Georgi-Glashow model and its SU(N)-generalization are explored at nonzero temperatures and in the regime when the Higgs boson is not infinitely heavy. The finiteness of the Higgs-boson mass leads to various novel effects. Those include the appearance of two separate phase transitions and of the upper bound on the parameter of the weak-coupling approximation, necessary to maintain the stochasticity of the Higgs vacuum. The modification of the finite-temperature behavior of the model emerging due to the introduction of massless quarks is also discussed.

hep-th↗

arXiv2002

String representation of the SU(N)-inspired dual Abelian-Higgs-type theory with the $Θ$-term

String representation of the $[U(1)]^{N-1}$ gauge-invariant dual Abelian-Higgs-type theory, which is relevant to the SU(N)-QCD with the $Θ$-term and provides confinement of quarks, is derived. The N-dependence of the Higgs vacuum expectation value is found, at which the tension of the string joining quarks becomes N-independent, similarly to the real QCD. Contrary to that, the inverse coupling constant of the rigidity term of this string always behaves approximately as 1/N. A long-range Aharonov-Bohm-type interaction of a dyon (i.e., a quark which acquired a magnetic charge due to the $Θ$-term) with a closed electric string becomes nontrivial at $Θ$ not equal to $Nπ$ times an integer. On the contrary, at these critical values of $Θ$, the scattering of dyons over strings is absent.

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