2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51887The construction of a $N_T=3$ cohomological gauge theory on an hyper-K"ahler eight-fold, whose group theoretical descrition was given by Blau and Thompson, is performed explicitly.13 pages, LATEX; addition of an appendix, mild change of title, some improvements of textHigh Energy Physics - TheoryEuclidean super Yang-Mills theory on a hyper-K"ahler manifoldtext