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

Maxwell, Katherine A.; Voronov, Alexander A.

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

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Maxwell, Katherine A.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2412.18585
(Preprint)

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2412.18585.pdf
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Maxwell, K. A., & Voronov, A. A. (submitted). The Neveu-Schwarz group and Schwarz's extended super Mumford form.

Cite as: https://hdl.handle.net/21.11116/0000-0010-5F70-6

Abstract

n 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.