  We study the confinement between vortex strings in the dual lattice gauge
theory of the abelian Higgs model. The dual lattice gauge theory is described
by a 2-form gauge field. We calculate the string-antistring potential from the
surface operator of the 2-form gauge field. The linear confining potential
appears in a confinement phase and it disappears in a deconfinement phase. The
phase diagram of the theory is also obtained.
