Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories

Abstract

We construct an $\epsilon$-deformation of W algebras, corresponding to the additive version of quiver ${\text{W}}_{q,t^{-1}}$ algebras which feature prominently in the 5d version of the BPS/CFT correspondence and refined topological strings on toric Calabi-Yau's. This new type of algebras fill in the missing intermediate level between $q$-deformed and ordinary W algebras. We show that $\epsilon$-deformed W algebras are spectral duals of conventional W algebras, in particular the $\epsilon$-deformed conformal blocks manifestly reproduce instanton partition functions of 4d $\mathcal{N}=2$ quiver gauge theories in the full $\Omega$-background and give dual integral representations of ordinary W conformal blocks.

arXiv commentv1: 50 pages. v2: published version

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Cited by in corpus (5)

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• Gauge origami and quiver W-algebras
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Bispectral duality and separation of variables from surface defect transition