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arXiv · 2412.18585

The Neveu-Schwarz group and Schwarz's extended super Mumford form

Katherine A. Maxwell·Alexander A. Voronov
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Abstract

In 1987, Albert Schwarz suggested a formula which extends the super Mumford form from the moduli space of super Riemann surfaces into the super Sato Grassmannian. His formula is a remarkably simple combination of super tau functions. We compute the Neveu-Schwarz action on super tau functions, and show that Schwarz's extended Mumford form is invariant under the the super Heisenberg-Neveu-Schwarz action, which strengthens Schwarz's proposal that a locus within the Grassmannian can serve as a universal moduli space with applications to superstring theory. Along the way, we construct the Neveu-Schwarz, super Witt, and super Heisenberg formal groups.

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Katherine A. Maxwell, Alexander A. Voronov. 2024-12-24. The Neveu-Schwarz group and Schwarz's extended super Mumford form. https://arxiv.org/abs/2412.18585

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