Spectral Duality in 2d CFT: Yangian W Algebras and Dual-AGT Correspondence.

Abstract

Inspired by Seiberg-Witten integrable systems featuring in 4d N=2 quiver gauge theories and the AGT correspondence linking the latter to 2d CFT with higher spin symmetry, a Yangian or ε-deformation of W algebras is proposed. These are argued to be (bi-)spectral dual to ordinary conformal W algebras, in particular, the ε-deformed conformal blocks manifestly reproduce instanton partition functions (in the combinatorial form) or give dual Mellin-Barnes-like integral representations of 2d CFT correlators. The role of the new algebras in Calogero-Moser-Sutherland and Ruijsenaars-Schneider many-body integrable systems is also explored. This Dual-AGT perspective points towards an alternative approach to 2d CFT when other methods fail, akin to massless factorized scattering and form factor theory.