A bound on the superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, vertical bar < W >vertical bar < 1/2f(a)F, where f(a) and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss several possible applications.