Completing the square to find the supersymmetric matter effective action induced by coupling to linearized N=1 supergravity

We consider generic N = 1 supersymmetric matter coupled to Linearized N = 1 supergravity through the multiplet of currents. By completing the square, we find the effective action giving the leading supergravity induced correction to thr matter dynamics, expressed explicitly as a quadratic form in the components of the current multiplet. The effective action is supersymmetry invariant through an interplay of the local terms arising from the auxiliary held couplings, and the: nonlocal terms arising from graviton and gravitino exchange, neither of which is separately invariant. Having an explicit form for the supergravity induced effective action is a first step in studying effects of supergravity corrections on dynamical supersymmetry breaking and condensate formation in supersymmetric matter dynamics. In the Appendixes we give explicit expressions: for the currents, in our notational conventions. in thr Wess-Zumino and supersymmetric Yang-Mills models. (C) 2001 Academic Press.