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

2024/12/24 by Maxwell, Katherine A., Voronov, Alexander A. · 1 citation
#81R10 #81R12 (Secondary) #81T30 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2412.18585

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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• Derived Methods in Supergeometry: Fundamental Classes and Cohomology

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