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We consider gauge field theories in $D>4$ following the Wilson RG approachand show that they possess the ultraviolet fixed points where the gaugecoupling is dimensionless in any space-time dimension. At the fixed point theanomalous dimensions of the field and vertex operators are known exactly. Thesefixed points are nonperturbative and correspond to conformal invarianttheories. The same phenomenon also happens in supersymmetric theories with theYukawa type interactions.Comment: LaTeX, 10pp. v2: Comments and references adde

Ultraviolet fixed points in gauge and susy field theories in extra dimensions