The Exact superconformal R symmetry maximizes a
Apr, 200320 pages
Published in:
- Nucl.Phys.B 667 (2003) 183-200
e-Print:
- hep-th/0304128 [hep-th]
Report number:
- UCSD-PTH-03-02
View in:
Citations per year
Abstract:
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) \equiv (9 Tr R^3-3 Tr R)/32. The maximal value of a_{trial} is then, by a result of Anselmi et. al., the central charge \it{a} of the SCFT. Our a_{trial} maximization principle almost immediately ensures that the central charge \it{a} decreases upon any RG flow, since relevant deformations force a_{trial} 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 \it{a} and \it{c}, are always algebraic numbers.- 11.25.Hf
- 11.40.-q
- 11.30.Pb
- field theory: conformal
- supersymmetry
- R parity
- fermion: flavor
- anomaly
- renormalization group: transformation
- particle: multiplet
References(18)
Figures(0)