Schwarz, Albert Noncommutative supergeometry and duality. (English) Zbl 0967.58004 Lett. Math. Phys. 50, No. 4, 309-321 (1999). Summary: We introduce a notion of \(Q\)-algebra that can be considered as a generalization of the notion of \(Q\)-manifold (a supermanifold equipped with an odd vector field obeying \(\{Q,Q\}=0\)). We develop the theory of connections on modules over \(Q\)-algebras and prove a general duality theorem for gauge theories on such modules. This theorem contains as a simplest case \(SO(d,d,\mathbb{Z})\)-duality of gauge theories on noncommutative tori. Cited in 1 ReviewCited in 9 Documents MSC: 58A50 Supermanifolds and graded manifolds 58B34 Noncommutative geometry (à la Connes) 81R60 Noncommutative geometry in quantum theory 81T13 Yang-Mills and other gauge theories in quantum field theory Keywords:noncommutative geometry; supergeometry; Yang-Mills theory; duality PDFBibTeX XMLCite \textit{A. Schwarz}, Lett. Math. Phys. 50, No. 4, 309--321 (1999; Zbl 0967.58004) Full Text: DOI arXiv