We present results on an extended supergravity theory which has an internal SO(4) symmetry. All terms in the Lagrangian and transformation rules are determined through order κ², and some κ³ terms in L are given. A complicated feature of this theory, not present in previous extended supergravity models, is a strongly indicated nonpolynomial structure in the scalar fields. This theory contains as a special case SO(2) extended supergravity coupled to its Abelian vector multiplet.
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Ashok Das (1977) studied this question.
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