Vanishing trace anomaly in flat spacetime

Abstract

Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be understood as a way to define a subset in the infinite space of nonrenormalizable models of certain type. The subset realizes the demand that renormalization scale, along with any other dimensionful parameters, should be interpreted as a dynamical field's homogeneous background. This restriction is most straightforwardly implemented using dimensional regularization but it can hypothetically be imposed with any regularization method. Theories that satisfy it offer a new perspective on the radiative violation of global scale symmetry associated with RGE functions. As a result of the quantum scale invariant regularization being implemented, the scale symmetry is preserved at the quantum level despite the RGE functions being non-zero, as can be inspected at the level of composite quantum operators that govern dilatation of Green functions. We analyze these statements in explicit detail using a specific but easily generalized toy model with scalar fields.

arXiv commentSome added commentary, extended bibliography, typos corrected

References in corpus (15)

• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Quantum scale invariance, cosmological constant and hierarchy problem
• Scale invariance, unimodular gravity and dark energy
• Higgs-Dilaton Cosmology: From the Early to the Late Universe
• Higgs-Dilaton Cosmology: an effective field theory approach
• Scale-Independent Inflation and Hierarchy Generation
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• No fifth force in a scale invariant universe
• On the geometrical interpretation of scale-invariant models of inflation
• Manifestly scale-invariant regularization and quantum effective operators
• Inflation in a scale invariant universe
• Two-loop scale-invariant scalar potential and quantum effective operators
• Running couplings with a vanishing scale anomaly
• Standard Model with spontaneously broken quantum scale invariance
• Quantum implications of a scale invariant regularisation

Cited by in corpus (8)

• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Scale-invariant alternatives to general relativity. III. The inflation--dark-energy connection
• Asymptotic Scale Invariance and its Consequences
• Trace anomaly and infrared cutoffs
• Quantum scale invariance in gauge theories and applications to muon production
• Spontaneous scale symmetry breaking at high temperature
• A Finite Energy-Momentum Tensor for the ${\varphi }^3$ theory in $6$ dimensions