Logarithmic intertwining operators and W(2,2p-1)-algebras

Details Logarithmic intertwining operators and W(2,2p-1)-algebras Logarithmic intertwining operators and W(2,2p-1)-algebras

2007-02-04

arxiv.org/abs/math/0702081v2

J.Math.Phys.48:073503,2007

Mathematics

Quantum Algebra

22 pages; v2: misprints corrected, other minor changes. Final version to appear in Journal of Math. Phys

Scientific paper

10.1063/1.2747725

For every $p \geq 2$, we obtained an explicit construction of a family of $\mathcal{W}(2,2p-1)$-modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual $\mathcal{W}(2,2p-1)$-modules, we described their internal structure, and computed their graded dimensions. In addition, we constructed certain hidden logarithmic intertwining operators among two ordinary and one logarithmic $\mathcal{W}(2,2p-1)$-modules. This work, in particular, gives a mathematically precise formulation and interpretation of what physicists have been referring to as "logarithmic conformal field theory" of central charge $c_{p,1}=1-\frac{6(p-1)^2}{p}, p \geq 2$. Our explicit construction can be easily applied for computations of correlation functions. Techniques from this paper can be used to study the triplet vertex operator algebra $\mathcal{W}(2,(2p-1)^3)$ and other logarithmic models.

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