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arXiv · 0806.3560

The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector

Drazen Adamovic·Antun Milas
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Abstract

We classify irreducible $σ$-twisted modules for the N=1 super triplet vertex operator superalgebra $\mathcal{SW}(m)$ introduced recently [Adamovic D., Milas A., Comm. Math. Phys., to appear, arXiv:0712.0379]. Irreducible graded dimensions of $σ$-twisted modules are also determined. These results, combined with our previous work in the untwisted case, show that the $SL(2,\mathbb{Z})$-closure of the space spanned by irreducible characters, irreducible supercharacters and $σ$-twisted irreducible characters is $(9m+3)$-dimensional. We present strong evidence that this is also the (full) space of generalized characters for $\mathcal{SW}(m)$. We are also able to relate irreducible $\mathcal{SW}(m)$ characters to characters for the triplet vertex algebra $\mathcal{W}(2m+1)$, studied in [Adamovic D., Milas A., Adv. Math. 217 (2008), 2664-2699, arXiv:0707.1857].

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Drazen Adamovic, Antun Milas. 2008-12-13. The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector. https://doi.org/10.3842/sigma.2008.087

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