Torsion action and its possible observables
  The methods of effective field theory are used to explore the theoretical and phenomenological aspects of the torsion field. Spinor action coupled to electromagnetic field and torsion possesses an additional softly broken gauge symmetry. This symmetry enables one to derive the unique form of the torsion action compatible with unitarity and renormalizability. It turns out that the antisymmetric torsion field is equivalent to an massive axial vector field. The introduction of scalars leads to serious problems which are revealed after the calculation of the leading two-loop divergences. Thus the phenomenological aspects of torsion may be studied only for the fermion-torsion systems. In this part of the paper we obtain an upper bounds for the torsion parameters using present experimental data on forward-backward Z-pole asymmetries, data on the experimental limits on four-fermion contact interaction (LEP, HERA, SLAC, SLD, CCFR) and also TEVATRON limits on the cross section of new gauge boson, which could be produced as a resonance at high energy $p\bar{p}$ collisions. The present experimental data enable one to put the limits on torsion parameters for the various range of the torsion mass. We emphasize that for the torsion mass of the order of the Planck mass no any independent theory for torsion is possible, and one must directly use string theory. 
A.S. Belyaev and I.L. Shapiro