The principal W-algebra of \mathfrakpsl_2|2

2025/09/05 by Fehily, Zachary, Raymond, Christopher, Ridout, David
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.04795

Abstract

We study the structure and representation theory of the principal W-algebra W^k_pr of V^k(\mathfrakpsl_2|2). The defining operator product expansions are computed, as is the Zhu algebra, and these results are used to classify irreducible highest-weight modules. In particular, for k = ± (1)/(2), W^k_pr is not simple and the corresponding simple quotient is the symplectic fermion vertex algebra. We use this fact, along with inverse hamiltonian reduction, to study relaxed highest-weight and logarithmic modules for the small N=4 superconformal algebra at central charges -9 and -3.

Citations

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Related

• On resolution of highest weight modules over the N=2 superconformal algebra
• On W-algebra extensions of (2,p) minimal models: p > 3
• Representations of N=2 superconformal vertex algebra
• A universal W-algebra for N=4 super Yang-Mills
• The structure of Zhu's algebras for certain W-algebras