Twisted modules for N=2 supersymmetric vertex operator superalgebras arising from finite automorphisms of the N=2 Neveu-Schwarz algebra

Details Twisted modules for N=2 supersymmetric vertex operator superalgebras arising from finite automorphisms of the N=2 Neveu-Schwarz algebra Twisted modules for N=2 supersymmetric vertex operator superalgebras arising from finite automorphisms of the N=2 Neveu-Schwarz algebra

2011-10-02

arxiv.org/abs/1110.0229v2

Mathematics

Quantum Algebra

42 pages. References added, typos corrected, and minor expository changes made

Scientific paper

Twisted modules for N=2 supersymmetric vertex operator superalgebras are classified for the vertex operator superalgebra automorphisms which are lifts of a finite automorphism of the N=2 Neveu-Schwarz Lie superalgebra representation. These include the Ramond-twisted sectors and mirror-twisted sectors for N=2 vertex operator superalgebras, as well as twisted modules related to more general "spectral flow" representations of the N=2 Neveu-Schwarz algebra. We construct examples of twisted modules for free and lattice N=2 vertex operator superalgebras for all the N=2 Neveu-Schwarz Lie superalgebra automorphisms of finite order. As a consequence, we also construct the Ramond-twisted sectors for free and lattice N=1 supersymmetric vertex operator superalgebras. We show that the lifting of the mirror automorphism for the N=2 Neveu-Schwarz algebra to an N=2 vertex operator superalgebra is not unique and that different mirror map vertex operator superalgebra automorphisms of an N=2 vertex operator superalgebra can lead to non-isomorphic mirror-twisted modules, as in the case of free and lattice N=2 vertex operator superalgebras.

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