Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras

Abstract

We discover a realisation of the affine Lie superalgebra sl(2|1) and of the exceptional affine superalgebra D(2|1;alpha) as vertex operator extensions of two affine sl(2) algebras with dual levels (and an auxiliary level 1 sl(2) algebra). The duality relation between the levels is (k+1)(k'+1)=1. We construct the representation of sl(2|1) at level k' on a sum of tensor products of sl(2) at level k, sl(2) at level k' and sl(2) at level 1 modules and decompose it into a direct sum over the sl(2|1) spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to the affine D(2|1;k') at level k is traced to properties of sl(2)+sl(2)+sl(2) embeddings into D(2|1;alpha) and their relation with the dual sl(2) pairs. Conversely, we show how the level k' sl(2) representations are constructed from level k sl(2|1) representations.

50 pages, Latex2e, 2 figures, acknowledgements added

References in corpus (3)

• Equivalence between Chain Categories of Representations of Affine sl(2) and N=2 Superconformal Algebras
• Characters of admissible representations of the affine superalgebra sl(2|1)
• Modular Transformations and Invariants in the Context of Fractional Level Affine sl(2|1;C)

Cited by in corpus (15)

• The Worldsheet Dual of the Symmetric Product CFT
• Higher-Level Appell Functions, Modular Transformations, and Characters
• Strings on ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Logarithmic lift of the su(2)_{-1/2} model
• Duality of subregular W-algebras and principal W-superalgebras
• The ^sl(2)+^sl(2)/^sl(2) Coset Theory as a Hamiltonian Reduction of ^D(2|1;α)
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• $N=4$ superconformal algebras and diagonal cosets
• On the semisimplicity of the category $K{L}_k$ for affine Lie superalgebras
• Embedding of the Lie superalgebra $D(2,1;\alpha )$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• A Bosonization of $U_q(\widehat{sl}(M|N))$
• Parafermionic Representation of the Affine $sl(2/1)$ Algebra at Fractional Level
• The Grassmannian VOA
• FZZ-triality and large $\mathcal{N}=4$ super Liouville theory