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

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.