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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?