Chern-Simons theory on supermanifolds

We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N = 1 D = 3 super-Chern-Simons theory.