Cosets from equivariant W-algebras

Abstract

The equivariant $\mathcal{W}$-algebra of a simple Lie algebra $\mathfrak{g}$ is a BRST reduction of the algebra of chiral differential operators on the Lie group of $\mathfrak{g}$. We construct a family of vertex algebras $A[\mathfrak{g},\kappa ,n]$ as subalgebras of the equivariant $\mathcal{W}$-algebra of $\mathfrak{g}$ tensored with the integrable affine vertex algebra $L_n(\check{\mathfrak{g}})$ of the Langlands dual Lie algebra $\check{\mathfrak{g}}$ at level $n\in {\mathbb{Z}}_{>0}$. They are conformal extensions of the tensor product of an affine vertex algebra and the principal $\mathcal{W}$-algebra whose levels satisfy a specific relation.

10 pages

References in corpus (3)

• Trialities of orthosymplectic $\mathcal{W}$-algebras
• On semisimplicity of module categories for finite non-zero index vertex operator subalgebras
• Quantum coordinate ring in WZW model and affine vertex algebra extensions

Cited by in corpus (1)

• Ordinary modules for vertex algebras of ${\mathfrak{osp}}_{1|2n}$