New methods for finding a $\mathcal{N}=2$ gauge theory at the level of a compact algebras

In the last decade, many attempts have been made to find a $\mathcal{N}=2$ gauge theory at the level of a compact algebras. One such attempt is the recent study of the $\mathcal{N}=2$ theory in $S_f$ compactified on $S^2 \times S^1$ which yields a $U(1)$ gauge theory. In this work, we present a method which is appropriate to all such attempts, and which has the advantage that the $\mathcal{N}=2$ theory is originally of type $(P,N)$, where $P$ is the rationally complex Kolmogorov-Smirnov type.