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

Abstract

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 = Nπ × integer. On the contrary, at these critical values of Θ, the scattering of dyons over strings is absent.

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

“…Referring the reader for the details of the subsequent integrations over B µ and h i µν to Refs. [116,123], we present here the final result. It has the form…”

“…As follows from this relation, for a given α, there exist (N − 1) non-vanishing coefficients s α i , which are equal to ± 1 N (for details, see Ref. [116]). Therefore, given the value of the coefficient in front ofL(Σ i , C), one concludes that for Θ N π × integer, dyons experience a long-range topological interaction with closed dual strings, in accordance with the general arguments presented in Ref.…”

“…Within the dual description at issue, where the gauge field A µ is replaced by the dual field B µ , an electrically charged particle, which propagates along a closed contour C, is described through the 't Hooft-loop (and not the Wilson-loop) average. Furthermore, for the sake of generality, we will consider now the case of a [U(1)] N −1 -invariant dual Abelian Higgs model, extended in addition by the Θ-term [116]. Therefore, the SU(N )-symmetry-breaking pattern in the case at issue is the same as in the above-considered SU(N )-invariant 3D Georgi-Glashow model.…”

“…Refs. [95,116]) that the London limit allows for a construction of an exact string representation of the 't Hooft-loop average (76). Furthermore, the consistency of the corresponding [U(1)] N −1 -invariant dual Abelian Higgs model with the Yang-Mills theory in the large-N limit requires the coupling to behave with the number of colors as = λ /N .…”

“…Following Refs. [95,116], we consider here the scaling behavior λ = O(N 2 ), in which case κ stays N -independent in the large-N limit, i.e., the increase of N does not make the London limit deeper.…”