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 $\mathcal{S}\mathcal{W}(m)$ 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 $\mathcal{S}\mathcal{W}(m)$. We are also able to relate irreducible $\mathcal{S}\mathcal{W}(m)$ 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].

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/

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• Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
• The N=1 triplet vertex operator superalgebras
• On the triplet vertex algebra W(p)
• Rationality, Regularity, and C_2-cofiniteness
• Spinor construction of the c = 1/2 minimal model
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Cited by in corpus (13)

• The N=1 triplet vertex operator superalgebras
• Modularity of logarithmic parafermion vertex algebras
• Logarithmic Superconformal Minimal Models
• Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector
• On W-algebras associated to (2,p) minimal models and their representations
• Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$
• The structure of Zhu's algebras for certain W-algebras
• C_2-cofinite W-algebras and their logarithmic representations
• Lattice construction of logarithmic modules for certain vertex algebras
• Simplicity of higher rank triplet W-algebras
• $N=1$ super Virasoro tensor categories
• Vertex Algebras $\mathcal{W}(p{)}^{A_m}$ and $\mathcal{W}(p{)}^{D_m}$ and Constant Term Identities
• On principal realization of modules for the affine Lie algebra $A_1^{(1)}$ at the critical level