Three Dimensional Gauge Theories and Monopoles

Abstract

The coulomb branch of $N=4$ supersymmetric Yang-Mills gauge theories in $d=2+1$ is studied. A direct connection between gauge theories and monopole moduli spaces is presented. It is proposed that the hyper-Kähler metric of supersymmetric $N=4$ $SU(N)$ Yang-Mills theory is given by the charge $N$ centered moduli space of BPS monopoles in $SU(2)$. The theory is compared to $N=2$ supersymmetric Yang-Mills theory in four dimensions through compactification on a circle of the latter. It is found that rational maps are appropriate to this comparison. A BPS mass formula is also written for particles in three dimensions and strings in four dimensions.

25 pages

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Cited by in corpus (50)

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• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• TASI Lectures on Solitons
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• BPS Monopoles
• Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory
• M-Theory Origin of Mirror Symmetry in Three Dimensional Gauge Theories
• Mirror Mirror On The Wall: On 2d Black Holes and Liouville Theory
• Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants
• Special geometry in hypermultiplets
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem
• Moduli Spaces of Instantons on the Taub-NUT Space
• Monopoles in String Theory
• Multi-monopoles and Magnetic Bags
• The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\times S^1$
• Moduli of Monopole Walls and Amoebas
• Orientifolds, M-Theory, and the ABCD's of the Enhancon
• Fivebrane Instanton Corrections to the Universal Hypermultiplet
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
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• The Hasse Diagram of the Moduli Space of Instantons
• Enhancons, Fuzzy Spheres and Multi-Monopoles
• Super Yang-Mills Theory with Impurity Walls and Instanton Moduli Spaces
• Monopole Bubbling via String Theory
• Two Dimensional Mirror Symmetry From M-theory
• D-Branes in Field Theory
• Singular Monopoles from Cheshire Bows
• Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• The Implicit Metric on a Deformation of the Atiyah-Hitchin Manifold
• Intersecting Branes, Domain Walls and Superpotentials in 3d Gauge Theories
• Coulomb Branches of Star-Shaped Quivers
• Superconformal Quantum Mechanics from M2-branes
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals
• Superconformal hypermultiplets in superspace
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• One Loop Effects in Various Dimensions and D-Branes
• Branes, Quivers, and the Affine Grassmannian
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• Effective Lagrangian for 3d N=4 SYM theories for any gauge group and monopole moduli spaces
• Asymptotic Dynamics of Monopole Walls
• Exact low-energy effective actions for hypermultiplets in four dimensions
• Wrapped D-Branes as BPS Monopoles: The Moduli Space Perspective
• An 8-dimensional Taub-NUT-like hyper-Kähler metric in harmonic superspace formalism