2026-09-18T19:06:29Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/733752022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Victor Kac.
Van Ekeren, Jethro (Jethro William)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-27T15:26:46Z
2012-09-27T15:26:46Z
2012
2012
http://hdl.handle.net/1721.1/73375
809689621
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.
134 p.
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Modular invariance for vertex operator superalgebras
Thesis
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Publication
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<Abstract>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.</Abstract>
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