Chiral superfields in N = 2 supergravity

The transformation laws of chiral (scalar) superfields with arbitrary Weyl weight w are determined for the U(2) superconformal theory. A superconformally invariant density is given for fields with w = 2. For w = 1 it is possible to have smaller irreducible multiplets. The full restriction upon which the chiral superfield becomes reducible is exhibited. These results define a complete calculus for the construction of invariant actions with chiral superfields. As an example we find the action for the vector gauge multiplet