The N=1 triplet vertex operator superalgebras

Abstract

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m\ge 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p\ge 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 πi}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.

53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CMP

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Cited by in corpus (3)

• The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
• On W-algebras associated to (2,p) minimal models and their representations
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory