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We couple the massless spin-(0^±,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.
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Ferrara et al. (1977) studied this question.
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