Supersymmetric W-algebras

Abstract

We develop 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 $\mathfrak{gl}(n+1|n).$

24pages

References in corpus (3)

• Field Algebras
• Supersymmetric vertex algebras
• Introduction to Vertex Algebras

Cited by in corpus (4)

• Exact Bremsstrahlung functions in ABJM theory
• Dirac reductions and Classical W-algebras
• Generators of Supersymmetric Classical $W$-algebras
• $N=1$ super Virasoro tensor categories