We present the gauge theory of the graded conformal group. It contains four real fields with spins 2, 3/2, 1, and {}. The theory is invariant under local proper conformal, scale, chiral, gravitational, and supersymmetry transformations. This is the first of a class of superunified field theories, possessing U(n) rather than O(n) internal gauge symmetries and without a cosmological constant. Unitarity, renormalizability, and asymptotic states and the cancellation of some complicated higher-order terms in one of the two supersymmetry variations remain to be investigated.
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Kaku et al. (1977) studied this question.
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