Konechny, A.; Schwarz, A. On \((k\oplus l|g)\)-dimensional supermanifolds. (English) Zbl 0937.58001 Wess, Julius (ed.) et al., Supersymmetry and quantum field theory. Proceedings of the D. Volkov Memorial seminar, Kharkov, Ukraine, January 5-7, 1997. Berlin: Springer. Lect. Notes Phys. 509, 201-206 (1998). A notion of \((k\oplus l|q)\)-dimensional supermanifold as a manifold having \(q\) odd coordinates and \(k + l\) even coordinates with \(l\) of them taking only nilpotent values is introduced. It is shown that in many cases rigorous definitions can be based on this notion. We show that this notion can be used to formulate superconformal field theories with different number of supersymmetries in holomorphic and antiholomorphic sectors.For the entire collection see [Zbl 0893.00046]. Reviewer: Steven Duplij (Kharkov) Cited in 5 Documents MSC: 58A50 Supermanifolds and graded manifolds 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 32C11 Complex supergeometry 32G81 Applications of deformations of analytic structures to the sciences Keywords:supermanifold; superconformal transformation; supermoduli space × Cite Format Result Cite Review PDF Full Text: arXiv