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

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dc.creatorAdamovic, Drazen
dc.creatorMilas, Antun
dc.date2007-02-04
dc.date2007-05-14
dc.date.accessioned2026-07-07T10:38:20Z
dc.date.available2026-07-07T10:38:20Z
dc.descriptionFor 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.
dc.description22 pages; v2: misprints corrected, other minor changes. Final version to appear in Journal of Math. Phys
dc.identifierhttps://arxiv.org/abs/math/0702081
dc.identifierhttp://arxiv.org/abs/math/0702081
dc.identifierJ.Math.Phys.48:073503,2007
dc.identifierdoi:10.1063/1.2747725
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180682
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.titleLogarithmic intertwining operators and W(2,2p-1)-algebras
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