Mathieu moonshine and Siegel Modular Forms
Abstract A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they m...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2021)050 |
| _version_ | 1818556952234426368 |
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| author | Suresh Govindarajan Sutapa Samanta |
| author_facet | Suresh Govindarajan Sutapa Samanta |
| author_sort | Suresh Govindarajan |
| collection | DOAJ |
| description | Abstract A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of M 24 in terms of products of standard modular forms. This provides a new proof of their modularity. |
| first_indexed | 2024-12-13T23:53:50Z |
| format | Article |
| id | doaj.art-3425f2f1c6ef446e89a254cd92b4334c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T23:53:50Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-3425f2f1c6ef446e89a254cd92b4334c2022-12-21T23:26:41ZengSpringerOpenJournal of High Energy Physics1029-84792021-03-012021313510.1007/JHEP03(2021)050Mathieu moonshine and Siegel Modular FormsSuresh Govindarajan0Sutapa Samanta1Department of Physics, Indian Institute of Technology MadrasSchool of Physical Sciences, Indian Association for the Cultivation of ScienceAbstract A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of M 24 in terms of products of standard modular forms. This provides a new proof of their modularity.https://doi.org/10.1007/JHEP03(2021)050Black Holes in String TheoryExtended Supersymmetry |
| spellingShingle | Suresh Govindarajan Sutapa Samanta Mathieu moonshine and Siegel Modular Forms Journal of High Energy Physics Black Holes in String Theory Extended Supersymmetry |
| title | Mathieu moonshine and Siegel Modular Forms |
| title_full | Mathieu moonshine and Siegel Modular Forms |
| title_fullStr | Mathieu moonshine and Siegel Modular Forms |
| title_full_unstemmed | Mathieu moonshine and Siegel Modular Forms |
| title_short | Mathieu moonshine and Siegel Modular Forms |
| title_sort | mathieu moonshine and siegel modular forms |
| topic | Black Holes in String Theory Extended Supersymmetry |
| url | https://doi.org/10.1007/JHEP03(2021)050 |
| work_keys_str_mv | AT sureshgovindarajan mathieumoonshineandsiegelmodularforms AT sutapasamanta mathieumoonshineandsiegelmodularforms |