2003/04/30 by Ken Intriligator, Brian Wecht · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/s0550-3213(03)00459-0
published as Nucl.Phys.B667:183-200,2003 · 23 pages, 1 figure. v2: added comments. v3: added comments
arxiv created 2003/07/23 · arxiv updated 2009/11/30
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 atrial(R) ≡ (9 Tr R3-3 Tr R)/32. The maximal value of atrial is then, by a result of Anselmi et. al., the central charge \ita of the SCFT. Our atrial maximization principle almost immediately ensures that the central charge \ita decreases upon any RG flow, since relevant deformations force atrial to be maximized over a subset of the previously possible R-symmetries. Using atrial 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 \ita and \itc, are always algebraic numbers.