Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_{2}$ Coordinates

Details Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_{2}$ Coordinates Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_{2}$ Coordinates

2009-04-12

arxiv.org/abs/0904.1848v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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.

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