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BERSHADSKY–POLYAKOV VERTEX ALGEBRAS AT POSITIVE INTEGER LEVELS AND DUALITY

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Abstract

We study the simple Bershadsky–Polyakov algebra 𝒲k = 𝒲k(sl3, fθ) at positive integer levels and classify their irreducible modules. In this way, we confirm the conjecture from [9]. Next, we study the case k = 1. We discover that this vertex algebra has a Kazama–Suzuki-type dual isomorphic to the simple affine vertex superalgebra Lk′ (osp(1|2)) for k′ = –5=4. Using the free-field realization of Lk′ (osp(1|2)) from [3], we get a free-field realization of 𝒲k and their highest weight modules. In a sequel, we plan to study fusion rules for 𝒲k.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000, Zagreb, Croatia

    DRAŽEN ADAMOVIĆ & ANA KONTREC

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  1. DRAŽEN ADAMOVIĆ
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  2. ANA KONTREC
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Correspondence to ANA KONTREC.

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Dražen Adamović is supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund – the Competitiveness and Cohesion Operational Programme (KK.01.1.1.01.0004).

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ADAMOVIĆ, D., KONTREC, A. BERSHADSKY–POLYAKOV VERTEX ALGEBRAS AT POSITIVE INTEGER LEVELS AND DUALITY. Transformation Groups 28, 1325–1355 (2023). https://doi.org/10.1007/s00031-022-09721-z

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