3d N=2 brane webs and quiver matrices

We discuss 3d brane webs and effective Chern-Simons levels for 3d N = 2 gauge theories. We find that turning on real masses for chiral multiplets leads to various equivalent brane webs that are related by flipping positions of D5-branes. We interpret flips as ST-transformations for chiral multiplets. ST-transformations could turn abelian theories into dual theories with mixed Chern-Simons levels that are interpreted as quiver matrices C-ij encoding DT-invariants. We notice that each brane web corresponds to a quiver matrix. ST-transformations of holomorphic blocks are discussed to verify results. We also discuss the movement of flavor D5-branes, which leads to double-layer brane webs and manifests fiber-base duality. In the second part, we compute refined vortex partition functions of nonabelian theories with the gauge group U(N) and find corresponding quiver matrices. The computation shows that on Higgs branch nonabelian groups are broken to abelian groups.

Automated summary

This paper discusses 3D brane webs and effective Chern-Simons levels for 3D N=2 gauge theories. It is found that introducing real masses for chiral multiplets leads to equivalent brane webs that can be related by flipping positions of D5-branes. These flips are interpreted as ST-transformations for chiral multiplets, which can turn abelian theories into dual theories with mixed Chern-Simons levels. Each brane web corresponds to a quiver matrix C-ij encoding DT-invariants. The paper also discusses ST-transformations of holomorphic blocks and the movement of flavor D5-branes, which leads to double-layer brane webs and fiber-base duality.