Two-loop low-energy effective actions in $ \mathcal{N}=2 $ and $ \mathcal{N}=4 $ three-dimensional SQED

Abstract

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.