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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].

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