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We consider compactifications induced by the gravitino field of elevendimensional supergravity. Such compactifications are not trivial in the sensethat the gravitino profiles are not related to pure bosonic ones by means of asupersymmetry transformation. The basic property of such backgrounds is thatthey admit $\psi$-torsion although they have vanishing Riemann tensor. Thus,these backgrounds may be considered also as solutions of the teleparallelformulation of supergravity. We construct two classes of solutions, one withboth antisymmetric three-form field, gravity and gravitino and one with onlygravity and gravitino. In these classes of solutions, the internal space is aparallelized compact manifold, so that it does not inherit any cosmologicalconstant to the external spacetime. The latter turns out to be flat Minkowskiin the maximally symmetric case. The elimination of the cosmological constantin the spontaneously compactified supergravity seems to be a generic propertybased on the trading of the cosmological constant for parallelizing torsion.

Vanishing Cosmological Constant by Gravitino-Dressed Compactification of 11D Supergravity