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We study four dimensional $N=2$ supersymmetric gauge theories on R³ × S¹ with a circle of radius R. They interpolate between four dimensional gauge theories (R=∞) and $N=4$ supersymmetric gauge theories in three dimensions ($R=0$). The vacuum structure can be determined quite precisely as a function of R, agreeing with three and four-dimensional results in the two limits.
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Seiberg et al. (1996) studied this question.