’t Hooft surface in lattice gauge theory

We discuss the lattice formulation of the’t Hooft surface, that is, the two-dimensional surface operator of a dual variable. The’t Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the’t Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.