arXiv subjects

Dmitri Antonov

Publications and source records attributed to Dmitri Antonov.

At least 37 records · Page 2Linked to original sources

arXiv2002

Higgs-inspired corrections to the RG flow in the finite-temperature 3D Georgi-Glashow model and its SU(N)-generalization

The Berezinsky-Kosterlitz-Thouless (BKT) RG flow in the ensemble of monopoles existing in the finite-temperature (2+1)D Georgi-Glashow model is explored in the regime when the Higgs field is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W-boson. The corrections to the standard RG flow are derived to the leading order in the inverse mass of the Higgs boson. According to the obtained RG equations, the scaling of the free-energy density in the critical region and the value of the critical temperature of the phase transition are found to be unaffected by the finiteness of the Higgs-boson mass. The evolution of the Higgs mass itself is also investigated and shown to be rather weak, that enables one to treat this parameter as a constant. The same analysis is further performed in the SU(N)-case at N>2, where the RG invariance is demonstrated to hold only approximately, in a certain sense. Modulo this approximation, the critical behaviour of the SU(N)-model turns out to be identical to that of the SU(2)-one.

hep-th↗

arXiv2002

Deconfining phase transition in the 3D Georgi-Glashow model with finite Higgs-boson mass

The (2+1)D Georgi-Glashow model is explored at finite temperature in the regime when the Higgs boson is not infinitely heavy. The resulting Higgs-mediated interaction of monopoles leads to the appearance of a certain upper bound for the parameter of the weak-coupling approximation. Namely, when this bound is exceeded, the cumulant expansion used for the average over the Higgs field breaks down. The finite-temperature deconfining phase transition with the account for the same Higgs-mediated interaction of monopoles is further analysed. It is demonstrated that in the general case, accounting for this interaction leads to the existence of two distinct phase transitions separated by the temperature region where W-bosons exist in both, molecular and plasma, phases. The dependence of possible ranges of the critical temperatures corresponding to these phase transitions on the parameters of the Georgi-Glashow model is discussed. The difference in the RG behaviour of the fugacity of W-bosons from the respective behaviour of this quantity in the compact-QED limit of the model is finally pointed out.

hep-th↗

arXiv2002

Finite Temperature Behavior of the 3D Polyakov Model with Massless Quarks

The (2+1)D Georgi-Glashow (or Polyakov) model with the additional fundamental massless quarks is explored at finite temperature. In the case of vanishing Yukawa coupling, it is demonstrated that the interaction of a monopole and an antimonopole in the molecule via quark zero modes leads to the decrease of the Berezinsky-Kosterlitz-Thouless critical temperature when the number of quark flavors is equal to one. If the number of flavors becomes larger, monopoles are shown to exist only in the molecular phase at any temperatures exceeding a certain exponentially small one. This means that for such a number of flavors and at such temperatures, no fundamental matter can be confined by means of the monopole mechanism.

hep-th↗

arXiv2002

Accounting for the finiteness of the Higgs-boson mass in the 3D Georgi-Glashow model

(2+1)-dimensional Georgi-Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU(N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colours. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colours to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colours.

hep-th↗

arXiv2001

Renormalization-group flow in the 3D Georgi-Glashow model

The renormalization-group (RG) flow in the finite-temperature (2+1)-dimensional Georgi-Glashow model is explored. This is done in the limit when the squared electric coupling constant is much larger than the mass of the Higgs field. The novel equation describing the evolution of the Higgs mass is derived and integrated along the separatrices of the RG flow in the limit when the original theory reduces to the 2D XY model. In particular, it is checked that in the vicinity of the phase-transition point, there exists a range of parameters allowing to the Higgs mass evolved along some of the separatrices to remain much smaller than the squared electric coupling constant.

hep-th↗

arXiv2001

Monopole potential and confining strings in the (2+1)-dimensional Georgi-Glashow model

Confining strings are investigated in the (2+1)D Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of the mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of the potential of monopole densities and string coupling constants are found as well.

hep-th↗

arXiv2001

Confining Membranes and Dimensional Reduction

The dual theory describing the 4D Coulomb gas of point-like magnetically charged objects, which confines closed electric strings, is considered. The respective generalization of the theory of confining strings to confining membranes is further constructed. The same is done for the analogous SU(3)-inspired model. We then consider a combined model which confines both electric charges and closed strings. Such a model is nothing, but the mixture of the above-mentioned Coulomb gas with the condensate of the dual Higgs field, described by the dual Abelian Higgs model. It is demonstrated that in a certain limit of this dual Abelian Higgs model, the system under study undergoes naively the dimensional reduction and becomes described by the (completely integrable) 2D sine-Gordon theory. In particular, owing to this fact, the phase transition in such a model must be of the Berezinskii-Kosterlitz-Thouless type, and the respective critical temperature is expressed in terms of the parameters of the dual Abelian Higgs model. However, it is finally discussed that the dimensional reduction is rigorously valid only in the strong coupling limit of the original 4D Coulomb gas. In such a limit, this reduction transforms the combined model to the 2D free bosonic theory.

hep-th↗

arXiv2001

Confining strings and RG flow in the (2+1)-dimensional Georgi-Glashow model and its SU(3)-generalization

Confining strings and RG flow at finite temperature are investigated in the (2+1)-dimensional Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of the potential of monopole densities and string coupling constants are found. At finite temperature, the mass of the Higgs field scales according to a novel RG equation. It is checked that in the limit when the original theory is reduced by the RG flow to the 2D XY model, the so-evolved Higgs mass is still much smaller than the squared electric coupling constant. The SU(3)-theory of confining strings is also discussed within the same approximations.

hep-th↗

arXiv2001

Confining strings in the Abelian-projected SU(3)-gluodynamics II. 4D-case with $θ$-term

The generalization of 4D confining string theory to the SU(3)-inspired case is derived. It describes string representation of the Wilson loop in the SU(3)-analogue of compact QED extended by the $θ$-term. It is shown that although the obtained theory of confining strings differs from that of compact QED, their low-energy limits have the same functional form. This fact leads to the appearance of the string $θ$-term in the low-energy limit of the SU(3)-inspired confining string theory. In particular, it is shown that in the extreme strong coupling regime, the crumpling of string world sheets could disappear owing to the string $θ$-term at $θ=π/12$. Finally, some characteristic features of the SU(N)-case are pointed out.

hep-ph↗

arXiv2001

A Possible Universal Treatment of the Field Strength Correlator in the Abelian-Projected SU(2)-Theory

An integral relation between two functions parametrizing the bilocal field strength correlator within the Stochastic Vacuum Model is obtained in the effective Abelian-projected SU(2)-theory. This relation is independent of the concrete properties of the ensemble of vortex loops, which are present in the theory under study. By virtue of the lattice result stating that the infrared asymptotic behaviours of these functions should have the same functional form, the obtained relation enables one to find these behaviours, as well as the infrared asymptotics of the bilocal correlator of densities of the vortex loops. Those turn out to be exponentials, decreasing at the inverse mass of the dual vector boson, times certain polynomials in the inverse integer powers of the distance. This result agrees with the general predictions and the existing lattice data better than the results of previous calculations, where these powers were found to be half-integer ones.

hep-ph↗

arXiv2000

Evaluation of Self-Intersecting Wilson Loop in the Stochastic Vacuum Model

A Wilson loop is evaluated within the stochastic vacuum model for the case when the respective contour is self-intersecting and its size does not exceed the correlation length of the vacuum. The result has the form of a certain functional of the tensor area. It is similar to that for the non-self-intersecting loop only when the contour is a plane one. Even for such a contour, the obtained expression depends on the ratio of two functions parametrizing the bilocal field strength correlator taken at the origin, which is not so for the case of non-self-intersecting contour.

hep-ph↗

arXiv2000

Topological and confining properties of Abelian-projected SU(3)-QCD

In this talk, we discuss several topics related to the Abelian-projected SU(3)-QCD. First of them is the Aharonov-Bohm effect emerging during the extension of this theory by the introduction of the $Θ$-term. Another topic is devoted to various consequences of screening of the dual vector bosons by electric vortex loops. In particular, it is demonstrated that this effect modifies significantly the interaction of quarks. Next, the influence of screening to electric and magnetic field correlators in the four-dimensional Abelian-projected SU(3)-QCD is studied. Finally, the bilocal correlator of electric field strengths in the three-dimensional gas of SU(3) Abelian-projected monopoles is discussed.

hep-ph↗

arXiv2000

String Representation of Gauge Theories

In this talk, various approaches to the problem of evaluation of the field strength correlators in the SU(3)-gluodynamics, which play the major role in the Stochastic Vacuum Model, are reviewed. This is done in the framework of the effective Abelian-projected theories under the various assumptions implied on the properties of the ensemble of Abelian-projected monopoles. In particular, within the assumption on the condensation of the monopole Cooper pairs, the main method of investigation is the string representation of field strength correlators. The calculation of the bilocal field strength correlator in the 3D effective theory, where Abelian-projected monopoles are assumed to form a gas, based on the string representation for the Wilson loop in this theory, is also presented.

hep-ph↗

arXiv2000

Field Correlators in Abelian-Projected Theories and Stochastic Vacuum Model

The bilocal electric field strength correlators in Abelian-projected SU(2)- and SU(3)-theories are derived with accounting for the contributions to these quantities brought about by the virtual vortex loops, built out of the dual Nielsen-Olesen strings. Owing to the screening of magnetic charge of the dual vector bosons in the gas of such loops, these bosons become heavier, which leads to the respective change of the correlation length of the vacuum in the models under study. Besides that, it turns out that such a screening leads also to the appearance of the long-range contribution to one of the two coefficient functions, which parametrize the bilocal correlator within the Stochastic Vacuum Model. Finally, the modifications of the propagators of the dual vector bosons, inspired by the correlation effects in the gas of vortex loops, are also discussed.

hep-ph↗

arXiv2000

Confining Strings in the Abelian-Projected SU(3)-Gluodynamics

String representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the monopole condensation. It is demonstrated that the summation over world sheets, bounded by the contour of the Wilson loop, is realized by the summation over branches of a certain effective multivalued potential of the monopole densities. Finally, by virtue of the so-constructed representation of the Wilson loop in terms of the monopole densities, this quantity is evaluated in the approximation of a dilute monopole gas, which makes confinement in the model under study manifest.

hep-th↗

arXiv2000

String Nature of Confinement in (Non-)Abelian Gauge Theories

Recent progress achieved in the solution of the problem of confinement in various (non-)Abelian gauge theories by virtue of a derivation of their string representation is reviewed. The theories under study include QCD within the so-called Method of Field Correlators, QCD-inspired Abelian-projected theories, and compact QED in three and four space-time dimensions. Various nonperturbative properties of the vacua of the above mentioned theories are discussed. The relevance of the Method of Field Correlators to the study of confinement in Abelian models, allowing for an analytical description of this phenomenon, is illustrated by an evaluation of field correlators in these models.

hep-th↗

arXiv2000

Testing Nonperturbative Ansaetze for the QCD Field Strength Correlator

A test for the Gaussian and exponential Ansaetze for the nonperturbative parts of the coefficient functions, D^{nonpert.} and D_1^{nonpert.}, which parametrize the gauge-invariant bilocal correlator of the field strength tensors in the stochastic vacuum model of QCD, is proposed. It is based on the evaluation of the heavy-quark condensate within this model by making use of the world-line formalism and equating the obtained result to the one following directly from the QCD Lagrangian. This yields a certain relation between D^{nonpert.}(0) and D_1^{nonpert.}(0), which is further compared with an analogous relation between these quantities known from the existing lattice data. Such a comparison leads to the conclusion that at the distances smaller than the correlation length of the vacuum, Gaussian Ansatz is more suitable than the exponential one.

hep-ph↗

arXiv1999

The Abelian Higgs Model as an Ensemble of Vortex Loops

In the London limit of the Ginzburg-Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation- and translation invariant measure of integration over their shapes leads to effective sine-Gordon theories of the dual fields. The representations of the partition functions of both grand canonical ensembles are derived in the form of the integrals over the vortex dipoles and the small vortex loops, respectively. By virtue of these representations, the bilocal correlator of the vortex dipoles (loops) is calculated in the low-energy limit. It is further demonstrated that once the vortex dipoles (loops) are considered as such an ensemble rather than individual ones, the London limit of the Ginzburg-Landau theory (Abelian Higgs model) with external monopoles is equivalent up to the leading order in the inverse UV cutoff to the compact QED in the corresponding dimension with the charge of Cooper pairs changed due to the Debye screening.

hep-th↗