Hidden and explicit quantum scale invariance

Abstract

There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In this work, we study the effects of such scale invariant renormalisation procedures. On the one hand, an explicitly quantum scale invariant theory can emerge from the scale invariant renormalisation of a scale invariant Lagrangian. On the other hand, we show how a quantum scale invariant theory can equally emerge from a Lagrangian visibly breaking scale invariance renormalised with scale dependent renormalisation (such as the traditional MS-bar scheme). In this last case, scale invariance is hidden in the theory, in the sense that it only appears explicitly after renormalisation.

arXiv commentMinor changes, updated references, matches published version

References in corpus (39)

• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• Standard Model Higgs boson mass from inflation: two loop analysis
• Standard Model Higgs boson mass from inflation
• Conformal Symmetry and the Standard Model
• 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
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• Do experiments suggest a hierarchy problem?
• Scale invariant extension of the standard model with strongly interacting hidden sector
• Physical Naturalness and Dynamical Breaking of Classical Scale Invariance
• Equivalence of the Einstein and Jordan frames
• Dark matter and neutrino masses from a scale-invariant multi-Higgs portal
• Naturally Speaking: The Naturalness Criterion and Physics at the LHC
• The Minimal Scale Invariant Extension of the Standard Model
• Classical scale-invariance, the electroweak scale and vector dark matter
• A modified naturalness principle and its experimental tests
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Scale-Independent Inflation and Hierarchy Generation
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Quantum corrections in Higgs inflation: the real scalar case
• Inflation, quintessence, and the origin of mass
• UV (in)sensitivity of Higgs inflation
• Manifestly scale-invariant regularization and quantum effective operators
• Is there a new physics between electroweak and Planck scales?
• Frame Covariant Nonminimal Multifield Inflation
• Spontaneously Broken Conformal Symmetry: Dealing with the Trace Anomaly
• Quantum corrections in Higgs inflation: the Standard Model case
• On the Stability of Infinite Derivative Abelian Higgs
• Running couplings with a vanishing scale anomaly
• Where to look for solving the gauge hierarchy problem?
• Meaning of the field dependence of the renormalization scale in Higgs inflation
• Quantum scale invariance on the lattice
• Asymptotic safety and Conformal Standard Model
• Asymptotic Scale Invariance and its Consequences
• Quantum implications of a scale invariant regularisation
• Scale invariance and broken electroweak symmetry may coexist together

Cited by in corpus (18)

• Dynamically induced Planck scale and inflation in the Palatini formulation
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Weyl $R^2$ inflation with an emergent Planck scale
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Matter matters in Einstein-Cartan gravity
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Asymptotic Scale Invariance and its Consequences
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Dimensional regularization, Wilsonian RG, and the Naturalness/Hierarchy problem
• Dilaton-assisted generation of the Fermi scale from the Planck scale
• Testing scale-invariant inflation against cosmological data
• Higgs field in cosmology
• Physical Tuning and Naturalness
• Quantum scale invariance in gauge theories and applications to muon production
• Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions In Compact-Star Matter
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• Fifth forces and frame invariance
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications