Confining strings in the Abelian-projected SU(3)-gluodynamics II. 4D-case with $θ$-term

Abstract

The generalization of 4D confining string theory to the SU(3)-inspired case is derived. It describes string representation of the Wilson loop in the SU(3)-analogue of compact QED extended by the $θ$-term. It is shown that although the obtained theory of confining strings differs from that of compact QED, their low-energy limits have the same functional form. This fact leads to the appearance of the string $θ$-term in the low-energy limit of the SU(3)-inspired confining string theory. In particular, it is shown that in the extreme strong coupling regime, the crumpling of string world sheets could disappear owing to the string $θ$-term at $θ=π/12$. Finally, some characteristic features of the SU(N)-case are pointed out.