Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions

Abstract

According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to describe the metrics on their spaces of vacua by means of the hyperkähler quotient construction. To check the identification of moduli spaces a comparison is made with field theory predictions. For SU(2) theory with k fundamental hypermultiplets the Coulomb branch is expected to be the D_k ALF gravitational instanton, so our results lead to a construction of such spaces. In the special case of SU(2) theory with four or fewer fundamental hypermultiplets we calculate the complex structures on the moduli spaces and compare them with field-theoretical results. We also discuss some puzzles with brane realizations of three-dimensional N=4 theories.

26 pages, LaTeX, 6 figures; exposition improved

References in corpus (2)

• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• Monopoles and Instantons on Partially Compactified D-Branes

Cited by in corpus (57)

• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• Wild Quiver Gauge Theories
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Branes, Instantons, And Taub-NUT Spaces
• Gravitational Instantons of Type D_k
• Hyperkahler Metrics from Periodic Monopoles
• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• Nahm's equations, $N=1^{\ast }$ domain walls, and D-strings in $Ad{S}_{5}x{S}_5$
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Moduli Spaces of Instantons on the Taub-NUT Space
• Monopoles in String Theory
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• Parameter counting for singular monopoles on R^3
• Brane bending and monopole moduli
• On Yang--Mills instantons over multi-centered gravitational instantons
• Semiclassical framed BPS states
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• Super Yang-Mills Theory with Impurity Walls and Instanton Moduli Spaces
• Monopole Bubbling via String Theory
• Seiberg-Witten Theory and Integrable Systems
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Geometric construction of new Yang-Mills instantons over Taub-NUT space
• Singular Monopoles via the Nahm Transform
• 't Hooft Defects and Wall Crossing in SQM
• Singular Monopoles from Cheshire Bows
• Seiberg-Witten Theory and Calogero-Moser Systems
• The BPS Spectrum Generator In 2d-4d Systems
• Intersecting Branes, Domain Walls and Superpotentials in 3d Gauge Theories
• Questions on provisional Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• Gravitational instantons as models for charged particle systems
• Lectures on Microstate Geometries
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• New ${\text{AdS}}_2/{\text{CFT}}_1$ pairs from ${\text{AdS}}_3$ and monopole bubbling
• Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals
• Harmonic forms on ALF gravitational instantons
• One Monopole with k Singularities
• Wall Crossing from Dirac Zeromodes
• Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories
• Instantons on the Taub-NUT Space
• Branes, Quivers, and the Affine Grassmannian
• Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type $A$
• Yang-Mills instantons in Kaehler spaces with one holomorphic isometry
• Holography for field theory solitons
• A Journey Between Two Curves
• Dirac zero modes for Abelian BPS multimonopoles
• Connecting Localization and Wall-Crossing via D-Branes
• Umbral Moonshine and String Duality
• From spatially periodic instantons to singular monopoles
• Instantons and Bows for the Classical Groups
• Instantons with continuous conformal symmetries: Hyperbolic and singular monopoles and more, oh my!
• Supersymmetry of the D3/D5 Defect Field Theory
• Simulating Magnetic Monopole-Defect Dynamics
• A New Gauge-Theoretic Construction of 4-Dimensional Hyperkähler ALE Spaces