Decomposition of extended superfields into irreducible representations of supersymmetry

We give the decomposition of superfields with arbitrary Lorebtz and U(N) indices, in terms of irreducible representations of N extended [including U(N)] supersymmetry. The spectra of the superspin and super-U(N) Casimir operators as well as one missing label operator are given in closed form.     

Structure of the supergravity group

The supergravity group is found to be the direct product of general covariance groups in complex conjugated left and right handed superspaces. The ordinary space-time coordinate and the axial gravitational superfield are the real and imaginary part of the complex coordinate, respectively.     

Projection operators and supplementary conditions for superfields with arbitrary spin

It is shown that a superfield with an external spin j and a non-vanishing mass contains four irreducible representations of the supersymmetry algebra. A general method is proposed for extracting these irreducible multiplets out of the superfield using projection operators constructed with the help of Casimir operators. The same decomposition is expressed in terms of supplementary differential conditions.     

A superspace action for N = 2 supergravity

The action for N = 2 supergravity can be presented as the invariant volume of the chiral subspaces of the real N = 2 superspace. The invariant volume of the real superspace itself is shown to vanish. The real basis form of the action contains covariant Grassmann δ functions involving N = 2 prepotentials explicitly.