N=2 supersymmetric structures on classical W-algebras

2023/05/14 by Ragoucy, Eric, Song, Arim, Suh, Uhi Rinn
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2305.08087

Abstract

We describe an N=2 supersymmetric Poisson vertex algebra structure of N=1 (resp. N=0) classical W-algebra associated with \mathfraksl(n+1|n) and the odd (resp. even) principal nilpotent element. This N=2 supersymmetric structure is connected to the principal \mathfraksl(2|1)-embedding in \mathfraksl(n+1|n) superalgebras, which are the only basic Lie superalgebras that admit such a principal embedding.

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• Structures of (supersymmetric) classical W-algebras
• Supersymmetries in the theory of W-algebras
• Gelfand-Dickey Realizations of the supersymmetric classical W-algebras for \mathfrakgl(n+1|n) and \mathfrakgl(n|n)
• W-strings from N=2 Hamiltonian reduction and classification of N=2 super W-algebras
• The W algebra structure of N=2 CP_n coset models