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Moduli stacks of maps for supermanifolds. (English) Zbl 1312.14039

Summary: We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry of supermanifolds to include a treatment of super-stacks we prove that such moduli problems, under suitable conditions, give rise to Deligne-Mumford superstacks (where all of these objects have natural definitions in terms of super-geometry). We make some observations about the properties of these moduli super-stacks, as well as some remarks about their application in physics and their associated Gromov-Witten theory.

MSC:

14D23 Stacks and moduli problems
58A50 Supermanifolds and graded manifolds
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32C11 Complex supergeometry