The N=1 triplet vertex operator superalgebras

Understand

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, 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 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)).