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Turning on N=2 supersymmetry preserving relevant operators in a 4-dimensional N=2 superconformal field theory (SCFT) corresponds to a complex deformation compatible with the rigid special Kahler (RSK) geometry encoded in the low energy effective action. Field theoretic consistency arguments indicate that there should be many distinct such relevant deformations of each SCFT fixed point. Some new RSK-compatible complex deformations are constructed of isolated rank 1 SCFTs. We also make predictions for the dimensions of Higgs branches for some rank 1 SCFTs.

Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories