English

The N=1 triplet vertex operator superalgebras

Quantum Algebra 2009-04-17 v4 High Energy Physics - Theory Mathematical Physics math.MP Representation Theory

Abstract

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), m1m \geq 1, which are natural super analogs of the triplet vertex algebra family W(p), p2p \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)). This paper is a continuation of arXiv:0707.1857.

Keywords

Cite

@article{arxiv.0712.0379,
  title  = {The N=1 triplet vertex operator superalgebras},
  author = {Drazen Adamovic and Antun Milas},
  journal= {arXiv preprint arXiv:0712.0379},
  year   = {2009}
}

Comments

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