Logarithmic intertwining operators and vertex operators

Details Logarithmic intertwining operators and vertex operators Logarithmic intertwining operators and vertex operators

2006-09-11

arxiv.org/abs/math/0609306v2

Commun.Math.Phys.277:497-529,2008

Mathematics

Quantum Algebra

32 pages. To appear in CMP

Scientific paper

10.1007/s00220-007-0375-3

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.

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