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The N = 1 Triplet Vertex Operator Superalgebras

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Abstract

We introduce a newfamily of C 2-cofinite N = 1 vertex operator superalgebras \({\mathcal{SW}(m)}\), m ≥ 1, which are natural super analogs of the triplet vertex algebra family \({\mathcal{W}(p)}\), p ≥ 2, important in logarithmic conformal field theory. We classify irreducible \({\mathcal{SW}(m)}\)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible \({\mathcal{SW}(m)}\) characters. Finally, we contemplate possible connections between the category of \({\mathcal{SW}(m)}\)-modules and the category of modules for the quantum group \({U^{small}_q(sl_2)}\), \({q = e^{\frac{2 \pi i}{2m+1}}}\), by focusing primarily on properties of characters and the Zhu’s algebra \({A(\mathcal{SW}(m))}\). This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008).

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Dražen Adamović

  2. Department of Mathematics and Statistics, University at Albany (SUNY), Albany, NY, 12222, USA

    Antun Milas

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  1. Dražen Adamović
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  2. Antun Milas
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Correspondence to Antun Milas.

Additional information

Communicated by Y. Kawahigashi.

The second author was partially supported by NSF grant DMS-0802962.

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Adamović, D., Milas, A. The N = 1 Triplet Vertex Operator Superalgebras. Commun. Math. Phys. 288, 225–270 (2009). https://doi.org/10.1007/s00220-009-0735-2

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