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arXiv · 2208.10037

Orbifolds of Gaiotto-Rap\v{c}\'ak $Y$-algebras

Masoumah Al-Ali·Andrew R. Linshaw
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Abstract

The universal two-parameter ${\mathcal W}_{\infty}$-algebra is a classifying object for vertex algebras of type ${\mathcal W}(2,3,\dots, N)$ for some $N$. Gaiotto and Rap\v{c}\'ak recently introduced a large family of such vertex algebras called $Y$-algebras, which includes many known examples such as the principal ${\mathcal W}$-algebras of type $A$. These algebras admit an action of $\mathbb{Z}_2$, and in this paper we study the structure of their orbifolds. Aside from the extremal cases of either the Virasoro algebra or the ${\mathcal W}_3$-algebra, we show that these orbifolds are generated by a single field in conformal weight $4$, and we give strong finite generating sets.

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Masoumah Al-Ali, Andrew R. Linshaw. 2022-08-22. Orbifolds of Gaiotto-Rap\v{c}\'ak $Y$-algebras. https://doi.org/10.1016/j.jalgebra.2023.02.014

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