COSETS FROM EQUIVARIANT W-ALGEBRAS

The equivariant W-algebra of a simple Lie algebra g is a BRST reduction of the algebra of chiral differential operators on the Lie group of g. We construct a family of vertex algebras A[g, kappa, n] as subalgebras of the equivariant W-algebra of g tensored with the integrable affine vertex algebra L-n((sic)) of the Langlands dual Lie algebra (sic) at level n is an element of Z(>0). They are conformal extensions of the tensor product of an affine vertex algebra and the principal W-algebra whose levels satisfy a specific relation. When g is of type ADE, we identify A[g, kappa, 1] with the affine vertex algebra V kappa-1(g) circle times L-1(g), giving a new and efficient proof of the coset realization of the principal W-algebras of type ADE.

Automated summary

The paper introduces the equivariant W-algebra of a simple Lie algebra and constructs a family of vertex algebras that are subalgebras of the equivariant W-algebra tensor product with the Langlands dual Lie algebra's integrable affine vertex algebra. The levels of these vertex algebras satisfy specific relations. When the Lie algebra is of ADE type, a new proof of the coset realization of the principal W-algebras of ADE type is given.