Phenomenological Constraints to Dimensionality of the Spacetime with   Torsion
  Using the recent limits established by ATLAS to the contact four-fermion interaction, bounds on the size of the extra dimensions of space-time have been found, by assuming that the contact interactions come through the inclusion of torsion in the higher dimensional theory. For two extra dimensions, the limits are comparable to those in the literature, while for higher dimensional space-time, the volume of the extra dimensions is strongly constrained. 
Oscar Castillo-Felisola and Cristobal Corral and Ivan Schmidt and   Alfonso Zerwekh
hep-ph gr-qc hep-th