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

TL;DR

This paper explores the structure of conformal field theories with sl(2)_{-1/2} symmetry, revealing connections to the triplet W-algebra and proposing an augmented theory to better understand logarithmic extensions.

Contribution

It uncovers the triplet W-algebra within the coset construction of sl(2)_{-1/2} theories and introduces an augmented theory that characterizes the logarithmic lift.

Findings

The coset theory admits the triplet W-algebra as a chiral algebra.

An augmented sl(2)_{-1/2} theory is proposed to describe the logarithmic lift.

The structure of the triplet model is partially uncovered through parafermionic coset construction.

Abstract

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.