Twisted modules for N=2 supersymmetric vertex operator superalgebras arising from finite automorphisms of the N=2 Neveu-Schwarz algebra
arXiv:1110.0229
Abstract
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 present the construct of twisted modules for free N=2 vertex operator superalgebras for all of the N=2 Neveu-Schwarz Lie superalgebra automorphisms of finite order. We show how to extend these to lattice N=2 vertex operator superalgebras. 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 categories of mirror-twisted modules, as in the case of free and lattice N=2 vertex operator superalgebras.
42 pages. The shifts in the weight grading for some of the twisted modules are corrected. Clarifications in expositions added and minor typos corrected. Main results unchanged
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