Representation theory of the affine Lie superalgebra sl(2|1) at fractional level

Abstract

N=2 noncritical strings are closely related to the $\Slr/\Slr$ Wess-Zumino- Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the precise knowledge of the $\hslc$ representation theory at fractional level. In this paper, the embedding diagrams of singular vectors appearing in $\hslc$ Verma modules for fractional values of the level ($k=p/q-1$, p and q coprime) are derived analytically. The nilpotency of the fermionic generators in $\hslc$ requires the introduction of a nontrivial generalisation of the MFF construction to relate singular vectors among themselves. The diagrams reveal a striking similarity with the degenerate representations of the $N=2$ superconformal algebra.

Latex file, 31pp, 6 epsf figures uufiled

References in corpus (4)

• Conformal Blocks for admissible representations in SL(2) current algebra
• Analytic Expressions for Singular Vectors of the $N=2$ Superconformal Algebra
• Free field representations for the affine superalgebra sl(2|1)
• The Non-Critical N=2 String is an sl(2|1) Theory

Cited by in corpus (15)

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• On the SU(2|1) WZW model and its statistical mechanics applications
• Higher-Level Appell Functions, Modular Transformations, and Characters
• Resolutions and Characters of Irreducible Representations of the N=2 Superconformal Algebra
• The embedding structure of unitary N=2 minimal models
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras
• Characters of admissible representations of the affine superalgebra sl(2|1)
• On Principal Admissible Representations and Conformal Field Theory
• On osp(2|2) conformal field theories
• Coherent State Construction of Representations of osp(2|2) and Primary Fields of osp(2|2) Conformal Field Theory
• Admissible sl(2/1) Characters and Parafermions
• Modular Transformations and Invariants in the Context of Fractional Level Affine sl(2|1;C)
• A Bosonization of $U_q(\widehat{sl}(M|N))$
• Parafermionic Representation of the Affine $sl(2/1)$ Algebra at Fractional Level