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We discuss the non-perturbative behavior of the U(1)_R symmetry in N=2superconformal Chern-Simons theories coupled to matter in the (anti)fundamentaland adjoint representations of the gauge group, which we take to be U(N).Inequalities constraining this behavior are obtained as consequences ofspontaneous breaking of supersymmetry and Seiberg duality. This informationreveals a web of RG flows connecting different interacting superconformal fieldtheories in three dimensions. We observe that a subclass of these theoriesadmits an ADE classification. In addition, we postulate new examples of Seibergduality in N=2 and N=3 Chern-Simons-matter theories and point out interestingparallels with familiar non-perturbative properties in N=1 (adjoint) SQCDtheories in four dimensions where the exact U(1)_R symmetry can be determinedusing a-maximization.

R-charges, Chiral Rings and RG Flows in Supersymmetric Chern-Simons-Matter Theories