slˆ(2)−1/2 and the triplet model

Conformal field theories with slˆ(2)−1/2 symmetry are studied with a view to investigating logarithmic structures. Applying the parafermionic coset construction to the non-logarithmic theory, a part of the structure of the triplet model is uncovered. In particular, the coset theory is shown to admit the triplet W-algebra as a chiral algebra. This motivates the introduction of an augmented slˆ(2)−1/2-theory for which the corresponding coset theory is precisely the triplet model. This augmentation is envisaged to lead to a precise characterisation of the “logarithmic lift” of the non-logarithmic slˆ(2)−1/2-theory that has been proposed by Lesage et al.