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Twisted logarithmic modules of free field algebras

Given a non-semisimple automorphism φ of a vertex algebra V, the fields in a φ-twisted V-module involve the logarithm of the formal variable, and the action of the Virasoro operator L 0 on such a module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spac...

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Bibliographic Details
Published in:Journal of mathematical physics 2016-06, Vol.57 (6), p.1
Main Authors: Bakalov, Bojko, Sullivan, McKay
Format: Article
Language:English
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Summary:Given a non-semisimple automorphism φ of a vertex algebra V, the fields in a φ-twisted V-module involve the logarithm of the formal variable, and the action of the Virasoro operator L 0 on such a module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spaces when V is generated by free fields. Specifically, we consider the cases of symplectic fermions (odd superbosons), free fermions, and βγ-system (even superfermions). In each case, we determine the action of the Virasoro algebra.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4953249