String confinement in two-form lattice gauge theory

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