Confining strings in the Abelian-projected SU (3)-gluodynamics

Abstract

Abstract. -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.On the way of constructing the string representation of SU (3)-gluodynamics by means of the method of Abelian projections [1] (see Ref.[2] for recent reviews), the main results have up to now been obtained under the assumption of the monopole condensation. Indeed, this assumption leads to an effective Ginzburg-Landau type theory [3], whose string representation can further be investigated [4] analogously to that of the usual dual superconductor [5]. On the other hand, recently string representation of the Abelian-projected SU (2)-gluodynamics has been derived [6] under a weaker assumption, which states that Abelian-projected monopoles form a gas, rather than condense into the dual Higgs field. Such a way of treating Abelianprojected monopoles in the SU (2)-gluodynamics makes the string representation of the Wilson loop in this theory (which describes an external test particle, electrically charged w.r.t. the U (1) Cartan subgroup of SU (2)) similar to that of the Wilson loop in compact QED [7]. The aim of the present Letter is to extend the results of Ref.[6] to the case of Abelian-projected SU (3)-gluodynamics in 2+1 dimensions and finally to emphasize confinement in this theory in the sense of the Wilson area law [8].Let us start our analysis with considering the pure monopole contribution to the action of this theory, keeping for a while aside the noncompact part of diagonal fields. (The off-diagonal fields are as usual disregarded on the basis of the so-called Abelian dominance hypothesis [9]. That is because they are argued to become very massive (and thus short-ranged) and therefore c EDP Sciences

Finite-Temperature Behavior of the (2+1)d Georgi-Glashow Model With and Without Quarks

“…. Note that this formula is valid also for the standard case N = 2 and reproduces the SU (3)-result of the compact-QED limit [ 16], [ 13] m 2 D = 3g 2 m ζ. The new parameter of the cumulant expansion,ζI (3) N (N − 1), will be exponentially small provided that at x ∼ 1/2,…”

World-Line Formalism: Non-Perturbative Applications

“…Such calculations have been initially performed in various Abelian models, where confinement is provided by the monopole condensation. Those include the 3D Georgi-Glashow model and the 4D compact QED [116,117], as well as the 4D dual Abelian Higgs model in the London limit and its [U (1)] N−1 -symmetric generalization [118][119][120][121][122]. In this way, it has been explicitly shown that the vacuum correlation lengths in all these models are equal to the inverse masses of the corresponding dual vector bosons.…”

Accounting for the Finiteness of the Higgs–boson Mass in the 3d Georgi–glashow Model

“…The string representation of the compact-QED limit has been studied for the SU(3)-case in ref. [11] both in 3D and 4D. Here, similarly to all the above-mentioned papers, we have assumed that W bosons corresponding to different root vectors have the same masses.…”