  We perform a path-integral analysis of the string representation of the dual
Abelian Higgs (DAH) model beyond the London limit, where the string describing
the vortex of a flux tube has a finite thickness. We show that besides an
additional vortex core contribution to the string tension, a modified Yukawa
interaction appears as a boundary contribution in the type-II dual
superconducting vacuum. In the London limit, the modified Yukawa interaction is
reduced to the Yukawa one.
