Generally covariant theories of gauge fields on superspace

Different variants of general covariant theory of superfields with nontrivial torsion and curvature tensors are discussed from the viewpoint of holonomy group. An example of the lagrangian is considered, which is quadratic with respect to the torsion tensor in linear approximation of weak fields with the interaction switched-off and includes free fields with spin two and the Rarita–Schwinger fields with spin 3/2.