I describe a recent lattice Monte Carlo study of the vortex tension in the three-dimensional U(1)+Higgs model. This theory is the low-energy effective theory of high-temperature scalar electrodynamics and its vortices correspond to cosmic strings. A non-perturbative definition was given for the tension, i.e. the mass per unit length of a vortex, and it was measured numerically at various values of the parameters. The tension has a natural connection to the phase structure of the theory.
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