Vortex equations in abelian gauged sigma-models

Abstract

We consider nonlinear gauged sigma-models with Kahler domain and target. For a special choice of potential these models admit Bogomolny (or self-duality) equations -- the so-called vortex equations. We find the moduli space and energy spectrum of the solutions of these equations when the gauge group is a torus T^n, the domain is compact, and the target is C^n or CP^n. We also obtain a large family of solutions when the target is a compact Kahler toric manifold.

v2: 60 pages, more details than in CMP version

References in corpus (3)

• Moduli Space of Non-Abelian Vortices
• The Spectrum of Bogomol'nyi Solitons in Gauged Linear Sigma Models
• Yang-Mills-Higgs theory for symplectic fibrations

Cited by in corpus (27)

• Solitons in the Higgs phase -- the moduli matrix approach --
• Moduli Space of Non-Abelian Vortices
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• On the L^2-metric of vortex moduli spaces
• Intersecting Solitons, Amoeba and Tropical Geometry
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models
• Gauge theory, calibrated geometry and harmonic spinors
• Relations among topological solitons
• Non-Abelian Monopoles in the Higgs Phase
• Non-Abelian Chern-Simons vortices with generic gauge groups
• Decomposing Instantons in Two Dimensions
• Fractional Skyrmions and their molecules
• Non-abelian vortices on compact Riemann surfaces
• Two Species of Vortices in a massive Gauged Non-linear Sigma Model
• Gauging the Poisson sigma model
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Twisting gauged non-linear sigma-models
• Self-dual effective compact and true compacton configurations in generalized Abelian Higgs models
• Non-integrability of Self-dual Yang-Mills-Higgs System
• The Volume of the Quiver Vortex Moduli Space
• The Lie algebroid Poisson sigma model
• Moduli Spaces of Abelian Vortices on Kahler Manifolds
• Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
• Non-abelian vortices, Hecke modifications and singular monopoles
• A topological gauged sigma-model
• The Berry connection of the Ginzburg-Landau vortices