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In the N=1 four-dimensional new-minimal supergravity framework, wesupersymmetrise the coupling of the scalar kinetic term to the Einstein tensor.This coupling, although introduces a non-minimal derivative interaction ofcurvature to matter, it does not introduce harmful higher-derivatives. For thisconstruction, we employ off-shell chiral and real linear multiplets. Physicalscalars are accommodated in the chiral multiplet whereas curvature resides in alinear one.

A New Class of Four-Dimensional N=1 Supergravity with Non-minimal Derivative Couplings