The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector

Abstract

We classify irreducible $\sigma$-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 $\sigma$-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 $\sigma$-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].Comment: This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA