F-term Hybrid Inflation in Effective Supergravity Theories

We show that the effective low energy supergravity theories which result from a generic string theory can provide a promising framework for models of hybrid inflation in which the potential energy which drives inflation originates from the F-term of the effective supergravity theory. In the class of models considered the inflaton is protected from receiving mass during inflation by a Heisenberg symmetry and the potential during inflation takes the positive definite form $V \sim |F|^2$, which allows the possibility that $V\ll m_{3/2}^2 M_P^2$. We discuss a toy example where this is realised, then describe the application of this result to realistic models focusing on a particular example in which the $\mu$ problem and the strong CP-problem are addressed.