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Higgsed network calculus

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arxiv 1812.11961 v3 pith:XYROFOSR submitted 2018-12-31 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords quiverblockscorrespondingexplaintheoriesw-algebrasalgebraapproach
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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.

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  1. Spiralling branes, affine qq-characters and elliptic integrable systems

    hep-th 2024-12 accept novelty 7.0 of 10

    Quantum toroidal algebra intertwiners reproduce Ruijsenaars-Schneider and Koroteev-Shakirov Hamiltonians, Shiraishi functions, and a new proof of the noncommutative Jacobi identity for affine qq-characters.

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