  We calculate some one loop corrections to the effective action of theories in
$d$ dimensions that arise on the dimensional reduction of a Weyl fermion in $D$
dimensions. The terms that we are interested in are of a topological nature.
Special attention is given to the effective actions of the super Yang Mills
theories that arise on dimensional reduction of the N=1 theory in six
dimensions or on the dimensional reduction of the N=1 theory in ten dimensions.
In the latter case we suggest an interpretation of the quantum effect as a
coupling of the gauge field on the brane to a relative background gauge field.
