Emerging Potentials in Higher-Derivative Gauged Chiral Models Coupled to N=1 Supergravity

We present a new method to introduce scalar potentials to gauge-invariant chiral models coupled to supergravity. The theories under consideration contain consistent higher-derivative terms which do not give rise to instabilities and ghost states. The chiral auxiliaries are not propagating and can be integrated out. Their elimination gives rise to emerging potentials even when there is not a superpotential to start with. We present the case of a single chiral multiplet with and without a superpotential and, in the gauged theory, up to two chiral multiplets coupled to supergravity with no superpotential. A general feature of the emergent potential is that it is negative defined leading to anti-de Sitter vacua. In the gauge models, competing D-terms may lift the potential leading to stable and metastable de Sitter and Minkowski vacua as well with spontaneously broken supersymmetry.