Two-loop low-energy effective actions in N =2 and N =4 three-dimensional SQED

We study two-loop Euler-Heisenberg effective actions in three-dimensional N =2 and N =4 supersymmetric quantum electrodynamics (SQED) without Chern-Simons term. We find exact expressions for propagators of chiral superfields interacting with slowly-varying N =2 gauge superfield. Using these propagators we compute two-loop effective actions in the N =2 and N =4 SQED as the functionals of superfield strengths and their covariant spinor derivatives. The obtained effective actions contain new terms having no four-dimensional analogs. As an application, we find two-loop quantum corrections to the moduli space metric in the N =2 SQED.