Orbifolds of Gaiotto-Rapčák Y-algebras

Abstract

The universal two-parameter W∞-algebra is a classifying object for vertex algebras of type W(2,3,…,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 W-algebras of type A. These algebras admit an action of Z2, and in this paper we study the structure of their orbifolds. Aside from the extremal cases of either the Virasoro algebra or the W3-algebra, we show that these orbifolds are generated by a single field in conformal weight 4, and we give strong finite generating sets.