Consistency of couplings in supergravity theory with propagating Lorentz connexion

Our theory of supergravity with propagating Lorentz connexion ω sub(μ)sup(rs) is a supersymmetric extension of the ''massless case'' of Poincare gauge theory. In such a case, it is necessary to verify the consistency of couplings between ω sub(μ)sup(rs)(or the vierbein e sub(μ)sup(m)) and spinor fields in the theory. We will show that in our supersymmetric theory the coupling consistency between ω sub(μ)sup(rs) and its spinor partner lambda sub(α)sup(rs)is in fact guaranteed up to the trilinear interaction order. (author)