Higgsing and Superpotential Deformations of ADE Superconformal Theories

We study large classes of renormalization group flows, driven by scalar expectation values or mesonic superpotential terms, away from the conformal fixed points of the 4d supersymmetric gauge theories with $ADE$-type superpotentials. The $a$-maximization procedure allows us to compute the $R$ charges and to check the $a$-theorem conjecture. For a theory obtained by Higgsing the $D_{k+2}$ theory, we use the magnetic dual description proposed by Brodie to determine the parameter region where the resulting theory is at a non-trivial conformal fixed point.