Logarithmic intertwining operators and vertex operators

Abstract

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1{)}_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1{)}_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.

32 pages. To appear in CMP

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Cited by in corpus (12)

• Tensor categories for vertex operator superalgebra extensions
• Schur-Weyl Duality for Heisenberg Cosets
• The N=1 triplet vertex operator superalgebras
• Tensor categories and the mathematics of rational and logarithmic conformal field theory
• Logarithmic Intertwining Operators and Genus-One Correlation Functions
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• The level two Zhu algebra for the Heisenberg vertex operator algebra
• Fusion rules for the Virasoro algebra of central charge 25
• Free Field Realisations of Staggered Modules in 2D Logarithmic CFTs
• Logarithmic Vertex Algebras
• Logarithmic intertwining operators and the space of conformal blocks over the projective line
• A generalization of intertwining operators for vertex operator algebras