No-scale supergravity with new Fayet-Iliopoulos term

We find a new class of N=1 no-scale supergravity models with F- and D-term supersymmetry breaking, using a new Fayet-Iliopoulos term. The minimal setup contains one U(1) vector multiplet and one neutral chiral multiplet parametrizing SL(2,R)/U(1) manifold, with constant superpotential and linear gauge kinetic function. In our construction the FI term is field-dependent, and one can obtain flat vanishing potential (Minkowski vacuum) with broken SUSY, and global SL(2,R) invariance (self-duality) of the bosonic equations of motion. The spectrum of the model includes a massive spin-1/2 field as well as a vector, a scalar, and a pseudo-scalar -- all classically massless. We discuss several modifications/extensions of the model as well as the introduction of matter fields. We also find a two-field extension of already existing no-scale model.