sl(2)_{-1/2} and the Triplet Model

Details sl(2)_{-1/2} and the Triplet Model sl(2)_{-1/2} and the Triplet Model

2010-01-22

arxiv.org/abs/1001.3960v2

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 3 figures, 1 table; v2 added refs to vertex algebra literature and a few comments

Scientific paper

Conformal field theories with sl(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 sl(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 sl(2)_{-1/2}-theory that has been proposed by Lesage et al.

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