On R-symmetric Fixed Points and Superconformality

Abstract

An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for over twenty years, a precise non-perturbative relation between scale and conformal invariance in higher dimensions has been lacking. In this note, we specialize to four dimensions and give a full quantum mechanical proof that certain unitary R-symmetric fixed points are necessarily superconformal. Among other consequences, this result implies that the infrared fixed points of N=1 supersymmetric quantum chromodynamics are superconformal.

21 pages; references added; brief additional comments; results unchanged

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Comments on Unparticles
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• Higher derivative corrections in holographic Zamolodchikov-Polchinski theorem

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• On Scale and Conformal Invariance in Four Dimensions
• Conformal Bootstrap in Three Dimensions?
• Scale without Conformal Invariance: An Example
• Scale without Conformal Invariance: Theoretical Foundations
• Scale without Conformal Invariance at Three Loops
• Limit Cycles in Four Dimensions
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Mapping Anomalous Currents in Supersymmetric Dualities
• Supercurrent, Supervirial and Superimprovement
• A Conjectured Bound on Accidental Symmetries
• Perturbative c-theorem in d-dimensions
• Minimal Distances Between SCFTs
• On Limit Cycles in Supersymmetric Theories
• Comments on Worldsheet Description of the Omega Background
• Comments on scale invariant but non-conformal supersymmetric field theories
• Conformal invariance of tensor bosons tree amplitudes
• Gravity Dual for Cyclic Renormalization Group Flow without Conformal Invariance
• Gravity Dual for Hofman-Strominger Theorem
• Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions
• Non-Perturbative Constraints on Light Sparticles from Properties of the RG Flow
• Scale without Conformal Invariance in bottom-up Holography