Scalar multiplet coupled to supergravity

We couple the massless spin-($0^{\pm }$,1/2) scalar multiplet of global supersymmetry to the gauge action of supergravity. The resulting locally supersymmetric Lagrangian and transformation laws are derived both in second- and first-order formalism. The results are valid for an arbitrary global internal-symmetry group. The commutator algebra is also obtained and has new features compared with previous models. The mass term of the scalar multiplet is also discussed.