Topological defects in lattice gauge theories

We present a non-perturbative formalism for measuring defect free energies (monopole mass or vortex tension) in three-dimensional SU(2)+adjoint Higgs models. Starting from twisted, translation invariant boundary conditions, w e perform a change of variables that allows us to express the defect free e nergies in terms of 't Hooft loops. We propose that the defect free energie s can be used to distinguish between phases in this model, and also more ge nerally in other gauge field theories where no local order parameters exist . In the case of monopoles, our construction can also be used in four-dimen sional pure-gauge SU(2) theory, where it gives the monopole mass in the max imally abelian gauge without the need of actually fixing the gauge in the s imulation. Moreover, the expression is manifestly independent of the choice of the abelian projection as long as it is compatible with the classical ' t Hooft-Polyakov solution.