Fixed points of semi-simple supersymmetric gauge theories

We study fixed points and phase diagrams of semi-simple supersymmetric gauge theories coupled to chiral superfields and a superpotential. Particular emphasis is put on new phenomena which arise due to the semi-simple nature of gauge interactions and the constraints dictated by supersymmetry, unitarity, and the $a$-theorem. Using field multiplicities as free parameters, we find all superconformal fixed points and classify theories according to their phase diagrams. Highlights include asymptotically free theories displaying a range of interacting fixed points in the IR, asymptotically non-free theories that become asymptotically safe due to residual interactions, UV-complete theories with gauge sectors that are simultaneously UV-free and IR-free, and theories that remain interacting both in the asymptotic UV and IR. Estimates for the sizes of conformal windows are also provided, and implications for model building are discussed.