Abstract
In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the n = 2 local conformal time supersymmetry, which is a subgroup of the four-dimensional spacetime supersymmetry. We show that the potential of the scalar matter fields is a function of the Kähler potential and of the arbitrary parameter . On the quantum level our model for the case is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.
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