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Supersymmetric W-algebras

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Abstract

We explain a general theory of W-algebras in the context of supersymmetric vertex algebras. We describe the structure of W-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the W-algebra associated with the odd principal nilpotent element of the Lie superalgebra \(\mathfrak {gl}(n+1|n)\).

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Alexander Molev

  2. Laboratoire de Physique Théorique LAPTh, CNRS, Université Savoie Mont Blanc, BP 110, 74941 Annecy-le-Vieux Cedex, France

    Eric Ragoucy

  3. Department of Mathematical Sciences and Research institute of Mathematics, Seoul National University, GwanAkRo 1, Gwanak-Gu, Seoul, 08826, Korea

    Uhi Rinn Suh

Authors
  1. Alexander Molev
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  2. Eric Ragoucy
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  3. Uhi Rinn Suh
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Correspondence to Uhi Rinn Suh.

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Molev, A., Ragoucy, E. & Suh, U.R. Supersymmetric W-algebras. Lett Math Phys 111, 6 (2021). https://doi.org/10.1007/s11005-020-01346-1

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