Abstract: | We present an algorithm to search for Lagrangian SCFTs conformally dual to a given theory. We search the space of possible Lagrangian theories for conformal theories with desired properties: in particular number of vector fields, number of chiral fields, and the first two terms in the series expansion of the Schur limit of the superconformal__ __index. We implement this algorithm to look for dual theories for some class S theories. Namely, for those theories with effective number of vector fields being 18 and 20. We find two possible new dualities relating gaugings of the R_{0,4} theory to quiver gauge theories. We also discuss a novel observation (examples of theories that have matching a, c anomalies, as well as the Schur limit of their index, but do not match in the full superconformal index). These relations invite more explorations. |