Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_2$ Coordinates

Abstract

We show that vortices of Yang-Mills-Higgs model in $R^2$ space can be regarded as instantons of Yang-Mills model in $R^2\times Z_2$ space. For this, we construct the noncommutative $Z_2$ space by explicitly fixing the $Z_2$ coordinates and then show, by using the $Z_2$ coordinates, that BPS equation for the vortices can be considered as a self-dual equation. We also propose the possibility to rewrite the BPS equations for vortices as ADHM equations through the use of self-dual equation.

19 pages, various arguments are added, the exposition is improved

References in corpus (8)

• TASI Lectures on Solitons
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• Integrability of Vortex Equations on Riemann Surfaces
• Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
• Quiver Gauge Theory and Noncommutative Vortices
• Multiple Layer Structure of Non-Abelian Vortex
• Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
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Cited by in corpus (3)

• Integrable vortex-type equations on the two-sphere
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
• Equivariance on Discrete Space and Yang-Mills-Higgs Model