Abstract
We show how to combine higgsed topological vertices introduced in [7] 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 mathcal{N} = 2 and mathcal{N} = 4 quiver gauge theories and demonstrate how 3d S-duality appears in our setup.
Highlights
Namely the Ding-Iohara-Miki (DIM) algebra [8, 9] and show that it describes surprisingly many brane pictures
We demonstrate that the extended formalism describes very general interacting D5-NS5-D3 brane systems
In this paper we have enriched the dictionary between Type IIB brane constructions and representations of DIM algebra
Summary
In [7] we have introduced the D3-NS5 junctions such as (1.5). Here we would like to add the. In this construction we have implicitly assumed that the 5-branes lie at the same value of t on the Rt line — otherwise they have no chance to meet. In section 4.2.2 we evaluate the universal DIM R-matrix R in the tensor product of the vertical and horizontal Fock representations
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