{"id":"hexagon/2610.00471","pdf":"https://hexagonmath.org/pdf/2610.00471v1","url":"https://hexagonmath.org/abs/2610.00471v1","tags":["math.RT","msc:81T60","msc:81T13","msc:15A66","msc:81R25","msc:83E15","Fierz identity","Majorana-Weyl spinors","division algebras","null projection"],"score":0,"title":"Supersymmetric Yang--Mills theories with several times reduce to ten dimensions","domain":"math-ph","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math-ph","summary":"Supersymmetric Yang--Mills theories in signatures with several times are built by restricting the gaugino to the kernel of $k$ mutually orthogonal null vectors and letting the supersymmetry close on translations contracted with their product. We prove that every theory of this kind, defined by five axioms that Nishino's construction satisfies, has residual dimension $s+t-2k$ equal to ten (or to two, a degenerate case), and that its null vectors can be real only if $k\\le\\min(s,t)$. The cubic fermion terms reduce to a Fierz identity on the residual spinors, and that identity forces the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}