The Infrared Physics of Bad Theories

We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCDtheories with $N_f$ fundamentals, building on the algebraic description of theCoulomb branch, and deduce the low energy physics in any vacuum from the localgeometry of the moduli space. We confirm previous claims for good and ugly SQCDtheories, and show that bad theories flow to the same interacting fixed pointsas good theories with additional free twisted hypermultiplets. A Seiberg-likeduality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: thespaces of vacua of the putative dual theories are different. However such badtheories have a distinguished vacuum, which preserves all the globalsymmetries, whose infrared physics is that of the proposed dual. We finallyexplain previous results on sphere partition functions and elucidate therelation between the UV and IR $R$-symmetry in this symmetric vacuum.