Relations between supersymmetric structures in UV and IR for $\mathcal{N}=4$ bad theories

Abstract

We investigate options for the structure of the infrared fixed points of $\mathcal{N}=4$ bad theories in three dimensions. Unitarity constraints allow a number of possibilities, not necessarily a product of an interacting $\mathcal{N}=4$ SCFT and free theories. For each option we provide relations between the UV and IR $R-$symmetry groups. For some of them we give examples. In particular, the $\mathcal{N}4$ SU(2) SYM with two fundamental hypermultiplets is an example of a bad theory which flows to an interacting irreducible SCFT in the IR. The question of whether all the options are realized remains open.