  When an abelian gauge theory with integer charges is spontaneously broken by
the expectation value of a charge Q field, there remains a Z_Q discrete
symmetry. In a supersymmetric theory, holomorphy adds additional constraints on
the operators that can appear in the effective superpotential. As a result,
operators with the same mass dimension but opposite sign charges can have very
different coupling strengths. In the present work we characterize the operator
hierarchies in the effective theory due to holomorphy, and show that there
exist simple relationships between the size of an operator and its mass
dimension and charge. Using such holomorphy-induced operator hierarchies, we
construct a simple model with a naturally small supersymmetric mu term. This
model also provides a concrete realization of late-time thermal inflation,
which has the ability to solve the gravitino and moduli problems of weak-scale
supersymmetry.
