W-Algebras Extending Affine gl(1|1)

Abstract

It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the operator product algebra are then calculated. Among these extensions, one finds four infinite families that seem to contain, as subalgebras, copies of the W^(2)_N algebras of Feigin and Semikhatov at various levels and central charges +/- 1.

12 pages. This is a proceedings article based on a talk by TC at the Ninth International Workshop "Lie Theory and its Applications in Physics" in Varna, Bulgaria (20--26 June, 2011)

References in corpus (7)

• sl^(2)_{-1/2}: A Case Study
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• Branes in the GL(1|1) WZNW-Model
• The GL(1|1)-symplectic fermion correspondence
• The Extended Algebra of the Minimal Models
• From world-sheet supersymmetry to super target spaces
• The Extended Algebra of the SU(2) Wess-Zumino-Witten Models

Cited by in corpus (9)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• Coset Constructions of Logarithmic (1,p)-Models
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Modular Transformations and Verlinde Formulae for Logarithmic $(p_{+},p_{-})$-Models
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
• Staggered modules of $N=2$ superconformal minimal models
• The Mock Modular Data of a Family of Superalgebras