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 (24)

• Simple current extensions beyond semi-simplicity
• The Nichols algebra of screenings
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
• 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
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond 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 $\widehat{osp(1,2)}$
• Some applications and constructions of intertwining operators in LCFT
• On the Feigin-Tipunin conjecture
• 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
• The Vertex Algebra $M(1{)}^{+}$ and Certain Affine Vertex Algebras of Level -1
• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
• Simplicity of higher rank triplet W-algebras
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• ADE subalgebras of the triplet vertex algebra W(p): A-series
• $N=1$ super Virasoro tensor categories
• False Theta Functions and the Verlinde formula
• New polar-finite forms of generalized Euler identities for $A_1^{(1)}$-string functions and mock theta conjecture-like identities
• Simple modules for Affine vertex algebras in the minimal nilpotent orbit