Modular invariance for vertex operator superalgebras
Name
809689621-MIT.pdf
Description
Full printable version
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6.21 MB
Format
Adobe PDF
Checksum (MD5)
8e4f0f6c705594dff35df473f8bb22bf
Author(s)
Van Ekeren, Jethro (Jethro William)
Advisor(s)
Victor Kac.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 133-134).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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