Localization of affine W-algebras

Abstract

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level.

arXiv comment36 pages

References in corpus (3)

• Quantum Reduction for Affine Superalgebras
• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Chiral de Rham complex

Cited by in corpus (10)

• Rationality of W-algebras: principal nilpotent cases
• Screening operators for W-algebras
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras
• Free field realisation of boundary vertex algebras for Abelian gauge theories in three dimensions
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Free field realisation and the chiral universal centraliser
• On free field realization of quantum affine $W$-algebras
• Connecting affine $\mathcal{W}$-algebras: A case study on ${\mathfrak{sl}}_4$