  The requirement that duality and renormalization group transformations
commute as motions in the space of a theory has recently been explored to
extract information about the renormalization flows in different statistical
and field theoretical systems. After a review of what has been accomplished in
the context of 2d sigma models, new results are presented which set up the
stage for a fully generic calculation at two-loop order, with particular
emphasis on the question of scheme dependence.
