Sean Carroll writes:

*"As can be seen from (1.2), in the definition of torsion (unlike that of the curvature)*

a single vector field such as X or Y serves both as a direction in spacetime along which

a covariant derivative is taken and as the object being differentiated. This is clearly only

possible when the vector field is a section of the tangent bundle rather than an “internal”

vector bundle; thus, the existence of torsion distinguishes the connection on the tangent

bundle from the connections familiar from conventional gauge theories."
Therefore you cannot, for example, describe Maxwell's electromagnetism as a torsion field.

As I recall Gennady tries to get fields like EM as torsion effects?

http://www.shipov.com/files/200506_news03.pdfhttp://www.americanantigravity.com/documents/Gennady-Shipov-2006.pdf