Abstract
Using a theorem by Bonora, Pasti and Tonin on the existence of a solution for D=11, N=1 Bianchi identities in the presence of the Lorentz-Chern-Simons form we found the explicit rheonomic parametrizations of all curvatures. This leads to a differential equation for the torsion field which we exhibit and also to the equations of motion whose form has not been worked out yet. We show how the lagrangian can be constructed and we argue that the presently constructed anomaly free supergravity contains all the terms of the heterotic string effective theory except those with a ζ(3) coefficient whose addition ought to be studied.
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