Mixed network calculus

Abstract

We show how to combine higgsed topological vertices introduced in our previous work with conventional refined topological vertices. We demonstrate that the extended formalism describes very general interacting D5-NS5-D3 brane systems. In particular, we introduce new types of intertwining operators of Ding-Iohara-Miki algebra between different types of Fock representations corresponding to the crossings of NS5 and D5 branes. As a byproduct we obtain an algebraic description of the Hanany-Witten brane creation effect, give an efficient recipe to compute the brane factors in 3d N=2 and N=4 quiver gauge theories and demonstrate how 3d S-duality appears in our setup.

23 pages

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Cited by in corpus (6)

• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Polynomial representations of classical Lie algebras and flag varieties
• Irreducible representations of simple Lie algebras by differential operators
• Intertwining operator and integrable hierarchies from topological strings