Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions

Abstract

We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_θx S^2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R^{2n}_θx S^2 and nonabelian vortices on R^{2n}_θ, which can be interpreted as a blowing-up of a chain of D0-branes on R^{2n}_θinto a chain of spherical D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.

45 pages, 4 figures; v2: minor corrections

Cited by in corpus (45)

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• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
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• Instanton Solutions from Abelian Sinh-Gordon and Tzitzeica Vortices
• Instantons on Special Holonomy Manifolds
• Non-Abelian Global Vortices
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• Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
• Instantons, Topological Strings and Enumerative Geometry
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
• Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
• Yang-Mills Instantons and Dyons on Group Manifolds
• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
• Quiver Gauge Theory and Conformality at the TeV Scale
• Covariant Quiver Gauge Theories
• Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories
• Geometry and Energy of Non-abelian Vortices
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
• Non-integrability of Self-dual Yang-Mills-Higgs System
• Mirror Symmetry in Emergent Gravity
• Construction of Noncommutative Instantons in 4k Dimensions
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• Noncommutative Instantons in Diverse Dimensions
• Noncommutative Instantons on CP^n
• Sasakian quiver gauge theories and instantons on the conifold
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• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
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• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• Fermionic Zero Modes in Gauge and Gravity Backgrounds on a Sphere
• Classification of BPS equations in higher dimensions
• A ladder of topologically non-trivial non-BPS states
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Non-abelian vortices on CP^1 and Grassmannians