On permutation-twisted free fermions and two conjectures

Katrina Barron, Nathan Vander Werf

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3 Scopus citations


We conjecture that the category of permutation-twisted modules for a multi-fold tensor product vertex operator superalgebra and a cyclic permutation of even order is isomorphic to the category of parity-twisted modules for the underlying vertex operator superalgebra. This conjecture is based on our observations of the cyclic permutation-twisted modules for free fermions as we discuss in this work, as well as previous work of the first author constructing and classifying permutation-twisted modules for tensor product vertex operator superalgebras and a permutation of odd order. In addition, we observe that the transposition isomorphism for two free fermions corresponds to a lift of the -1 isometry of the integral lattice vertex operator superalgebra corresponding to two free fermions under boson-fermion correspondence. We conjecture that all even order cyclic permutation automorphisms of free fermions can be realized as lifts of lattice isometries under boson-fermion correspondence. We discuss the role of parity stability in the construction of these twisted modules and prove that in general, parity-unstable weak twisted modules for a vertex operator superalgebras come in pairs that form orthogonal invariant subspaces of parity-stable weak twisted modules, clarifying their role in many other settings.

Original languageEnglish (US)
Article number012009
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - 2013
Externally publishedYes
Event41st International Conference on Integrable Systems and Quantum Symmetries, ISQS 2013 - Prague, Czech Republic
Duration: Jun 12 2013Jun 16 2013

ASJC Scopus subject areas

  • General Physics and Astronomy


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