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.

arXiv comment46 pages, 22 figures

References in corpus (55)

• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• The Refined Topological Vertex
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Knot Invariants and Topological Strings
• Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
• Branes, Superpotentials and Superconformal Fixed Points
• Vortex Counting and Lagrangian 3-manifolds
• Seiberg Duality in Chern-Simons Theory
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
• Comments on 3d Seiberg-like dualities
• Small Instantons, del Pezzo Surfaces and Type I' theory
• Holomorphic Blocks in Three Dimensions
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Factorisation of N = 2 theories on the squashed 3-sphere
• Three-Dimensional Gauge Dynamics from Brane Configurations with (p,q)-Fivebrane
• Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
• A & B model approaches to surface operators and Toda theories
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Higgs branch localization in three dimensions
• Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
• Dual Boundary Conditions in 3d SCFT's
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• Factorisation and holomorphic blocks in 4d
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Magnetic quivers for rank 1 theories
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• Knots-quivers correspondence
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• On F-term contribution to effective action
• BPS states, knots and quivers
• 3d N=2 mirror symmetry, pq-webs and monopole superpotentials
• Intersecting Surface Defects and Instanton Partition Functions
• Topological strings, strips and quivers
• Topological vertex formalism with O5-plane
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities
• 3d Mirror Symmetry from S-duality
• More on topological vertex formalism for 5-brane webs with O5-plane
• Instanton counting and O-vertex
• 3d Expansions of 5d Instanton Partition Functions
• Intersecting Defects and Supergroup Gauge Theory
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Surface defects on E-string from 5-brane webs
• 6d/5d exceptional gauge theories from web diagrams
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• 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