Holomorphic selection rules, the origin of the μ term, and thermal inflation

When an abelian gauge theory with integer charges is spontaneously broken bythe expectation value of a charge Q field, there remains a Z_Q discretesymmetry. In a supersymmetric theory, holomorphy adds additional constraints onthe operators that can appear in the effective superpotential. As a result,operators with the same mass dimension but opposite sign charges can have verydifferent coupling strengths. In the present work we characterize the operatorhierarchies in the effective theory due to holomorphy, and show that thereexist simple relationships between the size of an operator and its massdimension and charge. Using such holomorphy-induced operator hierarchies, weconstruct a simple model with a naturally small supersymmetric mu term. Thismodel also provides a concrete realization of late-time thermal inflation,which has the ability to solve the gravitino and moduli problems of weak-scalesupersymmetry.Comment: 18 pages, 1 figur