Effective Theory Description of Anomalous U(1) Supersymmetry Breaking and Its Embedding into Supergravity

We discuss the embedding of anomalous U(1) supersymmetry breaking into supergravity, working in the effective theory after integrating out a strongly interacting non-Abelian gauge sector. By explicitly performing the fine-tuning of the cosmological constant, we calculate the gravitino mass and the supergravity correction to the expectation value of the auxiliary field D, the latter of which was previously argued to give rise to a dominant source of soft scalar masses. Unlike the conventional scheme of the hidden-sector gaugino condensation, we generically find a rather large gravitino mass m 3/2 of order , expressed in terms of the scale of the gaugino condensation and the scale ξ of the Fayet-Iliopoulos term. The explicit solution is given for the constant added to the superpotential in order to cancel the vacuum energy. In particular, we identify the parameter region in which no solution is found, as well as the parameter region in which the vacuum energy vanishes without adding the constant term. We also show how the allowed parameter region is reduced by requiring the positivity of the D-term soft mass-squared. Finally, we briefly discuss the constraint on the dilaton Kähler potential when the dynamical effect of the dilaton is included.