Abstract
Recently proposed relations between the renormalization group functions of the soft supersymmetry breaking terms and those of a rigid theory allow one to consider a possibility of constructing a totally all loop finite N=1 SUSY gauge theory, including the soft SUSY breaking terms. The requirement of finiteness, which can be satisfied in previously constructed finite SUSY GUTs, imposes some constraints on the SUSY breaking parameters which, in the leading order, coincide with those originating from the supergravity and superstring-inspired models. Explicit relations between the soft terms, which lead to a completely finite theory in any loop order, are given.
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