VORTICES AS INSTANTONS IN NONCOMMUTATIVE DISCRETE SPACE:: USE OF Z2 COORDINATES.

We show that vortices of Yang–Mills–Higgs model in R² space can be regarded as instantons of Yang–Mills model in R² × Z₂ space. For this, we construct the noncommutative Z₂ space by explicitly fixing the Z₂ coordinates and then show, by using the Z₂ 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. [ABSTRACT FROM AUTHOR]