In the Abelian dual Higgs model with dual Dirac strings suggested by F
aber et al. [Nucl. Phys, B 475 (1996) 73] the quantum fluctuations of
the dual-vector and the Higgs fields around an Abrikosov flux line are
taken into account in one-loop approximation. The contribution to the
string energy induced by such fluctuations is computed. An important
role of quantum fluctuations for the formation of a linearly rising in
terquark potential is claimed. (C) 1997 Published by Elsevier Science
B.V.