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We consider target space duality transformations for heterotic sigma modelsand strings away from renormalization group fixed points. By imposing certainconsistency requirements between the T-duality symmetry and renormalizationgroup flows, the one loop gauge beta function is uniquely determined, withoutany diagram calculations. Classical T-duality symmetry is a valid quantumsymmetry of the heterotic sigma model, severely constraining itsrenormalization flows at this one loop order. The issue of heterotic anomaliesand their cancelation is addressed from this duality constraining viewpoint.Comment: 17 pages, Late

HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP