N=1 supergravity theories coupled to matter and duality transformations

The most general action for chiral and complex linear superfields coupled to the N=1 old minimal supergravity is given. Scalar potentials for pure complex linear and mixed cases are found. A condition for the breakdown of the duality transformation, which transforms a theory with complex linear superfields to one with chiral scalar superfields, is obtained. When this condition is satisfied, the potentials and couplings cannot be transformed, in general, into a Kähler form; examples are given. Some aspects of vanishing cosmological constant are considered in this context.