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

TL;DR

This paper derives a string representation of a dual Abelian-Higgs-type theory relevant to SU(N) QCD with a $ heta$-term, revealing N-dependence of string tension and dyon-string interactions, with implications for confinement and topological effects.

Contribution

It provides a novel string representation of the dual Abelian-Higgs theory incorporating the $ heta$-term, highlighting N-dependence and dyon interactions in the context of confinement.

Findings

String tension becomes N-independent at a specific Higgs vacuum expectation value.

The rigidity term's inverse coupling constant behaves approximately as 1/N.

A nontrivial long-range Aharonov-Bohm interaction occurs at certain $ heta$ values.

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 $\Theta$-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 $\Theta$-term) with a closed electric string becomes nontrivial at $\Theta$ not equal to $N\pi$ times an integer. On the contrary, at these critical values of $\Theta$, the scattering of dyons over strings is absent.