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A formulation of the N_T=1, D=8 Euclidean super Yang-Mills theory withgeneralized self-duality and reduced Spin(7)-invariance is given which avoidsthe peculiar extra constraints of Nishino and Rajpoot, hep-th/0210132. Itsreduction to 7 dimensions leads to the G_2-invariant N_T=2, D=7 superYang-Mills theory which may be regarded as a higher-dimensional analogue of theN=2, D=3 super-BF theory. When reducing further that G_2-invariant theory to 3dimensions one gets the N_T=2 super-BF theory coupled to a spinorialhypermultiplet.Comment: 9 pages, Late

G2-INVARIANT 7D EUCLIDEAN SUPER YANG–MILLS THEORY AS 7-DIMENSIONAL ANALOGUE OF 3D SUPER-BF THEORY

G₂-INVARIANT 7D EUCLIDEAN SUPER YANG–MILLS THEORY AS 7-DIMENSIONAL ANALOGUE OF 3D SUPER-BF THEORY