Modular invariance for vertex operator superalgebras
Author(s)
Van Ekeren, Jethro (Jethro William)![Thumbnail](/bitstream/handle/1721.1/73375/809689621-MIT.pdf.jpg?sequence=5&isAllowed=y)
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Victor Kac.
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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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 133-134).
Date issued
2012Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.