Modular invariance for vertex operator superalgebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2012
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| Online Access: | http://hdl.handle.net/1721.1/73375 |
| _version_ | 1826189477684445184 |
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| author | Van Ekeren, Jethro (Jethro William) |
| author2 | Victor Kac. |
| author_facet | Victor Kac. Van Ekeren, Jethro (Jethro William) |
| author_sort | Van Ekeren, Jethro (Jethro William) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T08:15:21Z |
| format | Thesis |
| id | mit-1721.1/73375 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:15:21Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/733752019-04-14T07:19:20Z Modular invariance for vertex operator superalgebras Van Ekeren, Jethro (Jethro William) Victor Kac. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 133-134). We generalize Zhu's theorem on modular invariance of characters of vertex operator algebras (VOAs) to the setting of vertex operator superalgebras (VOSAs) with rational, rather than integer, conformal weights. To recover SL₂ (Z)-invariance, it turns out to be necessary to consider characters of twisted modules. Initially we assume our VOSA to be rational, then we replace rationality with a different (weaker) condition. We regain SL₂(Z)-invariance by including certain 'logarithmic' characters. We apply these results to several examples. Next we define and study 'higher level twisted Zhu algebras' associated to a VOSA. Using a novel construction we compute these algebras for some well known VOAs. by Jethro Van Ekeren. Ph.D. 2012-09-27T15:26:46Z 2012-09-27T15:26:46Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73375 809689621 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 134 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Van Ekeren, Jethro (Jethro William) Modular invariance for vertex operator superalgebras |
| title | Modular invariance for vertex operator superalgebras |
| title_full | Modular invariance for vertex operator superalgebras |
| title_fullStr | Modular invariance for vertex operator superalgebras |
| title_full_unstemmed | Modular invariance for vertex operator superalgebras |
| title_short | Modular invariance for vertex operator superalgebras |
| title_sort | modular invariance for vertex operator superalgebras |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73375 |
| work_keys_str_mv | AT vanekerenjethrojethrowilliam modularinvarianceforvertexoperatorsuperalgebras |