• DOI:10.1063/1.2747725
• Corpus ID: 13047843

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

@article{Adamovi2007LogarithmicIO,
  title={Logarithmic intertwining operators and W(2,2p−1) algebras},
  author={Dra{\vz}en Adamovi{\'c} and Antun Milas},
  journal={Journal of Mathematical Physics},
  year={2007},
  volume={48},
  pages={073503-073503}
}

• Dražen Adamović, A. Milas
• Published 4 February 2007
• Mathematics
• Journal of Mathematical Physics

For every p⩾2, we obtained an explicit construction of a family of W(2,2p−1) modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual 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 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 cp,1=1−[6(p−1)2∕p], p⩾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 W(2,(2p−1)3) and other logarithmic models.