Modular invariance for vertex operator superalgebras

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2012

Author dc:creator

• Van Ekeren, Jethro (Jethro William)

Advisor dc:contributor.advisor

• Victor Kac.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/73375

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/73375