Scale without Conformal Invariance: An Example

Abstract

We give an explicit example of a model in D=4-epsilon space-time dimensions that is scale but not conformally invariant, is unitary, and has finite correlators. The invariance is associated with a limit cycle renormalization group (RG) trajectory. We also prove, to second order in the loop expansion, in D=4-epsilon, that scale implies conformal invariance for models of any number of real scalars. For models with one real scalar and any number of Weyl spinors we show that scale implies conformal invariance to all orders in perturbation theory.

13 pages, 2 figures, Erratum added

References in corpus (6)

• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• Limit Cycles and Conformal Invariance
• Tutorial on Scale and Conformal Symmetries in Diverse Dimensions
• Scale without Conformal Invariance: Theoretical Foundations
• On R-symmetric Fixed Points and Superconformality
• Higher derivative corrections in holographic Zamolodchikov-Polchinski theorem

Cited by in corpus (36)

• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• Comments on Holographic Entanglement Entropy and RG Flows
• Limit Cycles and Conformal Invariance
• On renormalization group flows and the a-theorem in 6d
• Effective Theory of a Light Dilaton
• The Renormalization Group and Weyl-invariance
• Conformal Bootstrap in Three Dimensions?
• Consequences of Weyl Consistency Conditions
• Scale without Conformal Invariance: Theoretical Foundations
• Scale without Conformal Invariance at Three Loops
• Limit Cycles in Four Dimensions
• RG flows, cycles, and c-theorem folklore
• Scale invariance vs conformal invariance
• A Conjectured Bound on Accidental Symmetries
• Perturbative c-theorem in d-dimensions
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
• Superembedding methods for 4d N-extended SCFTs
• Conformal scaling and the size of $m$-hadrons
• On Limit Cycles in Supersymmetric Theories
• Comments on scale and conformal invariance in four dimensions
• Superconformally Covariant OPE and General Gauge Mediation
• Scale vs Conformal invariance from Entanglement Entropy
• Perturbative Critical Behavior from Spacetime Dependent Couplings
• Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly
• 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 duals of cyclic RG flows, with strings attached
• Conformal invariance from scale invariance in non-linear sigma models
• Gravity Dual for Hofman-Strominger Theorem
• Cyclic unparticle physics
• Correlators in phase-ordering from Schrödinger-invariance
• Non-Perturbative Constraints on Light Sparticles from Properties of the RG Flow
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Covariant Fracton Electrodynamics in Six Dimensions
• Extended Conformal Symmetry in $d\ne 4$: Conformal Symmetry of Abelian Gauge Theory in the Physical Sector