Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions

Abstract

Theories of scalars and gravity, with an Einstein-Hilbert term and non-minimal interactions, $M^{2}R/2-\alpha {\varphi }^{2}R/12$, have graviton exchange induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $\alpha$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $\alpha$ is absent, for small steps in scale $\delta \mu /\mu$ infinitesimal contact terms $\sim \delta \alpha$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $\beta$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.

arXiv comment11 pages, 4 figures. arXiv admin note: text overlap with arXiv:2009.14782

References in corpus (29)

• Cosmology and the Fate of Dilatation Symmetry
• Quantum scale invariance, cosmological constant and hierarchy problem
• Higgs-Dilaton Cosmology: From the Early to the Late Universe
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• Dynamically Induced Planck Scale and Inflation
• Emergent scale symmetry: Connecting inflation and dark energy
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Scale-invariant alternatives to general relativity
• Scale-Independent Inflation and Hierarchy Generation
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential
• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• On the geometrical interpretation of scale-invariant models of inflation
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Manifestly scale-invariant regularization and quantum effective operators
• Standard Model in Weyl conformal geometry
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• Weyl $R^2$ inflation with an emergent Planck scale
• Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance
• Two-loop scale-invariant scalar potential and quantum effective operators
• Planck mass and inflation as consequences of dynamically broken scale invariance
• Evolving Planck Mass in Classically Scale-Invariant Theories
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Axion Induced Oscillating Electric Dipole Moments
• Axion Induced Oscillating Electric Dipole Moment of the Electron
• Two scalar fields inflation from scale-invariant gravity with modified measure
• $F(R)$ gravity in the early Universe: Electroweak phase transition and chameleon mechanism
• Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory
• Starobinksy Inflation, Gravitational Contact Terms and the Induced BEH Boson Mass

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• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• The Weyl Geometric Gravity black hole in light of the Solar System tests