2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54657We study four dimensional $N=2$ supersymmetric gauge theories on $R^3 \times S^1$ with a circle of radius $R$. They interpolate between four dimensional gauge theories ($R=\infty$) 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.37 pages, harvmacHigh Energy Physics - Theorytext