The principal W-algebra of $\mathfrak{psl}_{2|2}$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911544811454464 |
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| author | Fehily, Zachary Raymond, Christopher Ridout, David |
| author_facet | Fehily, Zachary Raymond, Christopher Ridout, David |
| contents | We study the structure and representation theory of the principal W-algebra $\mathsf{W}^{\mathsf{k}}_{\mathrm{pr}}$ of $\mathsf{V}^{\mathsf{k}}(\mathfrak{psl}_{2|2})$. 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 $\mathsf{k} = \pm \frac{1}{2}$, $\mathsf{W}^{\mathsf{k}}_{\mathrm{pr}}$ 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 $-3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The principal W-algebra of $\mathfrak{psl}_{2|2}$ Fehily, Zachary Raymond, Christopher Ridout, David Quantum Algebra High Energy Physics - Theory Mathematical Physics Representation Theory We study the structure and representation theory of the principal W-algebra $\mathsf{W}^{\mathsf{k}}_{\mathrm{pr}}$ of $\mathsf{V}^{\mathsf{k}}(\mathfrak{psl}_{2|2})$. 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 $\mathsf{k} = \pm \frac{1}{2}$, $\mathsf{W}^{\mathsf{k}}_{\mathrm{pr}}$ 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 $-3$. |
| title | The principal W-algebra of $\mathfrak{psl}_{2|2}$ |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2509.04795 |