Hierarchically Split Supersymmetry with Fayet-Iliopoulos D-terms in String Theory

Abstract

We show that in string theory or supergravity with supersymmetry breaking through combined F-terms and Fayet-Iliopoulos D-terms, the masses for charged scalars and fermions can be hierarchically split. The mass scale for the gauginos and higgsinos of the MSSM is controlled by the gravitino mass m_{3/2}, as usual, while the scalars get extra contributions from the D-terms of extra abelian U(1) factors, which can make them much heavier. The vanishing of the vacuum energy requires that their masses lie below {m_{3/2} M_{Pl}}^{1/2}, which for m_{3/2}=O(TeV) sets a bound of 10^{10-13} GeV. Thus, scalars with non-vanishing U(1) charges typically become heavy, while others remain light, producing a spectrum of scalars with masses proportional to their charges, and therefore non-universal. This is a modification of the split supersymmetry scenario, but with a light gravitino. We discuss how Fayet-Iliopoulos terms of this size can arise in orientifold string compactifications with D-branes. Furthermore, within the frame work of D-term inflation, the same vacuum energy that generates the heavy scalar masses can be responsible for driving cosmological inflation.