Higgsed network calculus

Abstract

We introduce a formalism for describing holomorphic blocks of 3d quiver gauge theories using networks of Ding-Iohara-Miki algebra intertwiners. Our approach is very direct and gives an explicit identification of the blocks with Dotsenko-Fateev type integrals for q-deformed quiver W-algebras. We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.

22 pages, v2: typos corrected, references added, v3: more typos corrected

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Cited by in corpus (10)

• A slow review of the AGT correspondence
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Mixed network calculus
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Super instanton counting and localization
• Polynomial representations of classical Lie algebras and flag varieties
• Irreducible representations of simple Lie algebras by differential operators
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Intertwining operator and integrable hierarchies from topological strings