Dmitri Antonov

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.

String representation of field correlators in the Dual Abelian Higgs Model

Abstract. By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and the Stochastic Model of the QCD vacuum.

String representation of field correlators in the SU(3) gluodynamics

Abstract The string representation of the Abelian projected SU(3)-gluodynamics partition function is derived by using the path-integral duality transformation. On this basis, we also derive analogous representations for the generating functionals of correlators of gluonic field strength tensors and monopole currents, which are finally applied to the evaluation of the corresponding bilocal correlators. The large distance asymptotic behaviours of the latter turn out to be in a good agreement with existing lattice data and the Stochastic Model of the QCD vacuum.

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

Abstract 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.

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.

A model for string-breaking in QCD

We present a model for string breaking based on the existence of chromoelectric flux tubes. We predict the form of the long-range potential and obtain an estimate of the string breaking length. A prediction is also obtained for the behaviour with temperature of the string breaking length near the deconfinement phase transition. We plan to use this model as a guide for a program of study of string breaking on the lattice.

Confining properties of Abelian-projected theories

Abstract. Representations of the Abelian-projected SU(2) and SU(3) gluodynamics in terms of the magnetic monopole currents are derived. Besides the quadratic part, the obtained effective actions contain interactions of these currents with the world-sheets of electric strings in four dimensions (4D) or electric vortex lines in three dimensions (3D). Next, we illustrate that 3D compact QED is a small gauge-boson mass limit of a 3D Abelian Higgs model with external monopoles and give a physical interpretation of the confining string theory as the integral over the monopole densities. Finally, we derive the bilocal field-strength correlator in the weak-field limit of 3D compact QED, which turns out to be in line with the one predicted by the stochastic vacuum model.

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 ~ 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.

Gluodynamics string as a low-energy limit of the universal confining string theory

An effective string theory emerging from the bilocal approximation to the Method of Vacuum Correlators in gluodynamics is shown to be well described by the 4D theory of the massive Abelian Kalb-Ramond field interacting with the string, which is known to be the low-energy limit of the Universal Confining String Theory. The mass of the Kalb-Ramond field in this approach plays the role of the inverse correlation length of the vacuum, and it is shown that in the massless limit string picture disappears. The background field method, known in the theory of nonlinear sigma models, is applied to derivation of the effective action, quadratic in quantum fluctuations around a given (e.g. minimal) string world-sheet.Abstract An effective string theory emerging from the bilocal approximation to the Method of Vacuum Correlators in gluodynamics is shown to be well described by the 4D theory of the massive Abelian Kalb-Ramond field interacting with the string, which is known to be the low-energy limit of the Universal Confining String Theory. The mass of the Kalb-Ramond field in this approach plays the role of the inverse correlation length of the vacuum, and it is shown that in the massless limit string picture disappears. The background field method, known in the theory of nonlinear sigma models, is applied to derivation of the effective action, quadratic in quantum fluctuations around a given (e.g. minimal) string world-sheet.

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.