Duality and the Renormalization Group

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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.
16 pages, TeX. Invited talk presented at the NATO Workshop ``New Developments in Quantum Field Theory'', Zakopane, Poland, June 14--20, 1997

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