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 Higgsmodels. Starting from twisted, translation invariant boundary conditions, weperform a change of variables that allows us to express the defect freeenergies in terms of 't Hooft loops. We propose that the defect free energiescan be used to distinguish between phases in this model, and also moregenerally in other gauge field theories where no local order parameters exist.In the case of monopoles, our construction can also be used in four-dimensionalpure-gauge SU(2) theory, where it gives the monopole mass in the maximallyAbelian gauge without the need of actually fixing the gauge in the simulation.Moreover, the expression is manifestly independent of the choice of the Abelianprojection as long as it is compatible with the classical 't Hooft-Polyakovsolution.Comment: 22 pages, 2 figures, JHEP style. Typos corrected, some clarifications and new references added. To appear in JHE