Superfield formulation of the simplest three-dimensional gauge theories and conformal supergravities

A superfield description of three-dimensional $N=1,2$ supersynnnetric Yang–Mills theories and supergravities is given. Manifestly supersymmetric expressions are obtained for the topological Chern–Simons terms in the $N=1$ theory using the technique of differential and integral forms on superspace. The topological mass term in $D=3$, $N=2$ Yang–Mills theory is constructed in terms of an unconstrained gauge prepotential. A formulation of $D=3$, $N=2$ supergravity is given in the Ogievetskii–Sokachev geometrical approach, and superfield equations of conformal supergravity are obtained.