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.

Minor corrections, final version to appear in J. Algebra

References in corpus (1)

• Trialities of $\mathcal{W}$-algebras

Cited by in corpus (1)

• Quantum toroidal algebras and solvable structures in gauge/string theory