$L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910613712666624 |
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| author | Ferrari, Andrea E. V. Suter, Aiden |
| author_facet | Ferrari, Andrea E. V. Suter, Aiden |
| contents | We verify a conjecture of Beem and the first author stating that a certain family of physically motivated BRST reductions of beta-gamma systems and free fermions is isomorphic to $L_1(\mathfrak{psl}_{n|n})$, and that its associated variety is isomorphic as a Poisson variety to the minimal nilpotent orbit closure $\overline{\mathbb{O}_{\mathrm{min}}(\mathfrak{sl}_n)}$. This shows in particular that $L_1(\mathfrak{psl}_{n|n})$ is quasi-lisse. Combining this with other results in the literature (in particular work of Ballin et al.), this paper provides a concrete and important example of how one can extract two symplectic dual varieties from a rather well-known vertex operator algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits Ferrari, Andrea E. V. Suter, Aiden Quantum Algebra High Energy Physics - Theory 17B69 (Primary) We verify a conjecture of Beem and the first author stating that a certain family of physically motivated BRST reductions of beta-gamma systems and free fermions is isomorphic to $L_1(\mathfrak{psl}_{n|n})$, and that its associated variety is isomorphic as a Poisson variety to the minimal nilpotent orbit closure $\overline{\mathbb{O}_{\mathrm{min}}(\mathfrak{sl}_n)}$. This shows in particular that $L_1(\mathfrak{psl}_{n|n})$ is quasi-lisse. Combining this with other results in the literature (in particular work of Ballin et al.), this paper provides a concrete and important example of how one can extract two symplectic dual varieties from a rather well-known vertex operator algebra. |
| title | $L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits |
| topic | Quantum Algebra High Energy Physics - Theory 17B69 (Primary) |
| url | https://arxiv.org/abs/2409.13028 |