Orbifolds of Gaiotto-Rapčák $Y$-algebras
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 Rapčák 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.10037
- arXiv:
- arXiv:2208.10037
- Bibcode:
- 2022arXiv220810037A
- Keywords:
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- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Mathematics - Representation Theory
- E-Print:
- Minor corrections, final version to appear in J. Algebra