The Neveu-Schwarz group and Schwarz's extended super Mumford form
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| Format: | Preprint |
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2024
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| _version_ | 1866916789241249792 |
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| author | Maxwell, Katherine A. Voronov, Alexander A. |
| author_facet | Maxwell, Katherine A. Voronov, Alexander A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Neveu-Schwarz group and Schwarz's extended super Mumford form Maxwell, Katherine A. Voronov, Alexander A. Algebraic Geometry High Energy Physics - Theory 81T30 (Primary), 81R10, 81R12 (Secondary) 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. |
| title | The Neveu-Schwarz group and Schwarz's extended super Mumford form |
| topic | Algebraic Geometry High Energy Physics - Theory 81T30 (Primary), 81R10, 81R12 (Secondary) |
| url | https://arxiv.org/abs/2412.18585 |