Mass of quantum topological excitations and order parameter finite size dependence

We consider the spontaneously broken regime of the $O(n)$ vector model in $d=n+1$ space-time dimensions, with boundary conditions enforcing the presence of a topological defect line. Comparing theory and finite size dependence of one-point functions observed in recent numerical simulations we argue that the mass of the underlying topological quantum particle becomes infinite when $d\geq 4$.