Abstract
The theory of confinement based on the stochastic field mechanism, known as the Field Corrleator Method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of material on the properties of confinement in QCD. We enumerateall these properties as 1)-7), and discuss beyond FCM two existing approaches: monopole based Dual Ginzburg-Landau (DGL) theory,and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its selfconsistency; in particular, it is shown that the string tension {\sigma} is the only scaleful parameter in the theory beyond fermion masses, and {\Lambda}_QCD is calculated explicitly to the lowest order in terms of {\sigma}. We also formulate physical consequences of confinement, such as string breaking,Regge trajectories, role of confinement in the perturbation theory, chiral symmetry breaking, confinement in the boosted systems etc. It is demonstrated that the FCM is a suitable tool for the solution of these problems.
Highlights
The problem of confinement and its internal structure remains an important issue nowadays, while this topic is studied in numerous papers for the last 45 years, starting from the first papers [1,2,3,4]
Since the first definition of confinement via the area law of the Wilson loop [1], the lattice analysis of confinement plays the most important role, which allows to define the most important properties of confinement and study this phenomenon quantitatively, see [12]. These studies allowed us to analyze the QCD vacuum configurations and to search for monopolelike degrees of freedom (d.o.f.), as it is done in the Abelian projection method (APM) [13], in the center vortex model [14], and the thick vortex model [15]
In the Appendix B we have shown that the correlator DE1 generates the instantaneous Coulomb interaction VcðrÞ plus vectorlike interaction VE1, entering the Polyakov loop, Lf 1⁄4 exp ð− V1ðE2ÞTð∞ÞÞ
Summary
The problem of confinement and its internal structure remains an important issue nowadays, while this topic is studied in numerous papers for the last 45 years, starting from the first papers [1,2,3,4]. As we demonstrate below, using the concrete gluelump structure of the field correlators developed in [33,34], the FCM satisfies all criteria This has allowed to calculate the confinement interaction at all distances, ensuring linear confinement for r > λ ∼ 0.1 fm, where λ is the inverse mass of the lowest gluelump, MGlp ≈ 2 GeV, calculated via string tension σ. As we shall show below, for the most general form of field correlators one obtains the circular color magnetic currents kD around flux tubes, which satisfy asymptotically the dual London’s equation rotkD 1⁄4 λ−2ED and there emerges picture of dual superconducting fluxes around the dual Abrikosov string In all this picture no magnetic monopole d.o.f. are needed, the only microscopic reason of confinement is the presence of the scalar DðzÞ in the vacuum correlator hFμνðxÞΦFλσðyÞi ∼ ðδδ − δδÞDðx − yÞ þ. The concluding section gives the summary of results and discussion of possible development
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