Perturbative aspects of the supersymmetric three-dimensional massive QED

We perform the study of perturbative aspects of a three-dimensional supersymmetric Maxwell-Chern-Simons-Proca theory minimally coupled to scalar superfields. Using the superfield formalism, we derive the propagators for both gauge and matter superfields and compute the leading quantum corrections to the effective action. The presence of the Proca-like term explicitly breaks gauge invariance, modifying the structure of the gauge superfield propagator and leading to an essentially new form of quantum contributions in comparison with the usual QED. We analyze the Feynman diagrams that contribute to the quadratic part of the effective action, obtaining corrections to both the kinetic and mass terms of the scalar superfields. Furthermore, we discuss the UV behavior of the model, considering its renormalization properties and the possibility of perturbative finiteness to all loop orders, similar to supersymmetric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>QED</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub></a:mrow></a:math>. Finally, we highlight potential applications of this model in condensed matter systems and possible connections with modified supersymmetric electrodynamics and dualities in lower-dimensional theories.