Looking for a reference which discusses vortex equations on a compact Riemann surface as dimensional reductions of the Seiberg-Witten equations on four manifolds.
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$\begingroup$ You need to detail what you mean by dimensional reduction. $\endgroup$– Liviu NicolaescuCommented Dec 29, 2021 at 8:03
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$\begingroup$ @LiviuNicolaescu SW equations can be applied on $\Sigma\times \mathbb{R}^2$, $\Sigma$ being a surface and the equations are invariant in the $\mathbb{R}^2$ direction. I also thought there's some standard way to do it mentioned here at point 3 :mathoverflow.net/a/115724/131004 $\endgroup$– ParthaCommented Dec 29, 2021 at 8:23
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$\begingroup$ The noncompactness adds a few difficulties $\endgroup$– Liviu NicolaescuCommented Dec 29, 2021 at 14:22
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$\begingroup$ I would be happy to find any other reduction may be from $\Sigma\times S^2$ or $\Sigma\times S^1\times S^1$ or any such form. I thought there must be some standard result as mentioned in the link I mentioned. $\endgroup$– ParthaCommented Dec 29, 2021 at 15:02
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$\begingroup$ Try here, and here. $\endgroup$– TyroneCommented Jan 7, 2022 at 13:58
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