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INVARIANT SUBALGEBRAS OF THE SMALL 𝒩 = 4 SUPERCONFORMAL ALGEBRA

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Abstract

Various aspects of orbifolds and cosets of the small 𝒩 = 4 superconformal algebra are studied. First, we determine minimal strong generators for generic and specific levels. As a corollary, we obtain the vertex algebra of global sections of the chiral de Rham complex on any complex Enriques surface. We also identify orbifolds of cosets of the small 𝒩 = 4 superconformal algebra with Com(Vℓ(𝔰𝔩2); Vℓ+1(𝔰𝔩2) ⊗ 𝒲–5/2(𝔰𝔩4; frect)) and in addition at special levels with Grassmanian cosets and principal 𝒲-algebras of type A at degenerate admissible levels. These coincidences lead us to a novel level-rank duality involving Grassmannian supercosets.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, Edmonton, AB, Canada

    THOMAS CREUTZIG & WOLFGANG RIEDLER

  2. Department of Mathematics, University of Denver, Denver, CO, USA

    ANDREW R. LINSHAW

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  1. THOMAS CREUTZIG
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  2. ANDREW R. LINSHAW
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  3. WOLFGANG RIEDLER
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Correspondence to THOMAS CREUTZIG.

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Thomas Creutzig is supported by NSERC Discovery Grant RES0048511.

Andrew R. Linshaw is supported by Simons Foundation Grant 635650 and NSF Grant DMS 2001484.

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CREUTZIG, T., LINSHAW, A.R. & RIEDLER, W. INVARIANT SUBALGEBRAS OF THE SMALL 𝒩 = 4 SUPERCONFORMAL ALGEBRA. Transformation Groups 27, 797–832 (2022). https://doi.org/10.1007/s00031-021-09652-1

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