The Neveu-Schwarz group and Schwarz's extended super Mumford form
Algebraic Geometry
2025-06-12 v2 High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.2412.18585,
title = {The Neveu-Schwarz group and Schwarz's extended super Mumford form},
author = {Katherine A. Maxwell and Alexander A. Voronov},
journal= {arXiv preprint arXiv:2412.18585},
year = {2025}
}
Comments
46 pages, minor edits to cocycle arguments