The exact superconformal R-symmetry maximizes a

An exact and general solution is presented for a previously open problem. We show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the R-symmetry, among all possibilities, which (locally) maximizes the combination of 't Hooft anomalies a(trial)(R) equivalent to (9TrR(3) - 3TrR)/32. The maximal value of a(trial) is then, by a result of Anselmi et al. the central charge a of the SCFT. Our a(trial) maximization principle almost immediately ensures that the central charge a decreases upon any RG flow, since relevant deformations force atrial to be maximized over a subset of the previously possible R-symmetries. Using a(trial) maximization, we find the exact superconformal R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N = 1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. Our result implies that N = 1 SCFTs are algebraic: the exact scaling dimensions of all chiral primary operators, and the central charges a and c, are always algebraic numbers. (C) 2003 Elsevier B.V. All rights reserved.