Quantum corrections to vortex masses and energies

We study the 2+1 dimensional abelian Higgs model defined on a spatial torus at critical self-coupling. We propose a method to compute the quantum contribution to the mass of the ANO vortex and to multi-vortex energies. The one-loop quantum correction to multi-vortex energies is computed analytically at the critical value of the torus area (Bradlow limit). For other values of the area one can set up an expansion around this critical area (Bradlow parameter expansion). The method is explained and the next-to-leading term explicitly evaluated. To this order, the resulting energies depend on the torus periods, but not on the vortex positions.