2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221175Inspired by ideas regarding Hermitian NxN matrix fields obeying a non-associative algebra, 3-dimensional N=8 SUSic field theories are proposed to on-shell represent subalgebras of OSp(8|2) and OSp(8|4) groups of SUSY transformations. They are theories of 8 scalar and 8 spinor fields with Yukawa, quartic and sextic self-interactions. The actions as their R-symmetry exhibit only SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphisms. It is argued that the number of degrees of freedom scale like N^{3/2}. There also exists an extra S_N permutation symmetry group.RevTeX 4, 10 pages; v2: Typo corrected; v3: Typo corrected, notes and references added; v4: Comments and references added, corrections implemented;High Energy Physics - Theorytext