3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices

Abstract

We discuss 3d brane webs and effective Chern-Simons levels for 3d $\mathcal{N}=2$ 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 $U\left(N\right)$ and find corresponding quiver matrices. The computation shows that on Higgs branch nonabelian groups are broken to abelian groups.

46 pages, 22 figures

References in corpus (11)

• The Refined Topological Vertex
• Seiberg Duality in Chern-Simons Theory
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• BPS states, knots and quivers
• Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• Intersecting Defects and Supergroup Gauge Theory
• 6d/5d exceptional gauge theories from web diagrams
• Intersecting Surface defects and 3d Superconformal indices
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models

Cited by in corpus (1)

• 3d defects in 5d: RG flows and defect F-maximization