Supergraph techniques for D=3, N=1 broken supersymmetric theories

We enlarge the usual D=3 N=1 supergraph techniques to include the case of (explicitly or spontaneously) broken supersymmetric gauge theories. To illustrate the utility of these techniques, we calculate the two-loop effective potential of the SQED₃ by using the tadpole and the vacuum bubble methods. In these methods, to investigate the possibility of supersymmetry breaking, the superfields must be shifted by θ_α dependent classical superfields (vacuum expectation values), what implies in the explicit breakdown of supersymmetry in the intermediate steps of the calculation. Nevertheless, after studying the minimum of the resulting effective potential, we find that supersymmetry is conserved, while gauge symmetry is dynamically broken, with a mass generated for the gauge superfield.