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

Dmitri Antonov
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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 $Θ$ not equal to $Nπ$ times an integer. On the contrary, at these critical values of $Θ$, the scattering of dyons over strings is absent.

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Dmitri Antonov. 2002-07-10. String representation of the SU(N)-inspired dual Abelian-Higgs-type theory with the $Θ$-term. https://doi.org/10.1016/s0370-2693(02)02412-7

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