The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories

Abstract

We use brane techniques to study the space of vacua of abelian 3d $\mathcal{N}=3$ gauge theories. The coordinates on these spaces are the vevs of chiral monopole and meson operators, which are realized in the type IIB brane configuration of the theory by adding semi-infinite $(1,k)$ strings or F1 strings. The study of various brane setups allows us to determine a basis of chiral operators and chiral ring relations relevant to each branch of vacua, leading to the algebraic description of these branches. The method is mostly graphical and does not require actual computations. We apply it and provide explicit results in various examples. For linear quivers we find that the space of vacua has in general a collection of Coulomb-like branches, a Higgs branch and mixed branches. For circular quivers we find an extra branch, the geometric branch, parametrized by monopoles with equal magnetic charges in all $U(1)$ nodes and meson operators. We explain how to include FI and mass deformations. We also study $\mathcal{N}=3$ theories realized with $(p,q)$ 5-branes.

arXiv comment78 pages, 41 figures

References in corpus (25)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Notes on Superconformal Chern-Simons-Matter Theories
• 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
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Hyper-Kahler manifolds and multiply-intersecting branes
• Deformations of Superconformal Theories
• Three-Dimensional Gauge Dynamics from Brane Configurations with (p,q)-Fivebrane
• Chiral flavors and M2-branes at toric CY4 singularities
• The Chern-Simons Coefficient in Supersymmetric Yang-Mills Chern-Simons Theories
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• Intersecting Branes
• T^σ_ρ(G) Theories and Their Hilbert Series
• Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
• Ring Relations and Mirror Map from Branes

Cited by in corpus (5)

• The Infrared Physics of Bad Theories
• The moduli spaces of S-fold CFTs
• N=2 Moduli of AdS4 vacua: A fine-print study
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories