The Renormalization Group, Systems of Units and the Hierarchy Problem

Abstract

In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be based on Newton's constant or on the Higgs mass. These quantities are not invariant under the RG, and the ratio between the units is scale-dependent. In the toy model, strong RG running occurs in the intermediate regime between the Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I model. Possible connections with the problem of the mass hierarchy are pointed out.

Plain TEX, 16 pages. Some revisions, some references added

References in corpus (2)

• Fixed Points of Higher Derivative Gravity
• Further Evidence for a Gravitational Fixed Point

Cited by in corpus (18)

• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Gravity and the standard model with neutrino mixing
• Quantum Einstein Gravity
• On the renormalization group flow of f(R)-gravity
• The Renormalization Group and Weyl-invariance
• Asymptotic Safety, Fractals, and Cosmology
• Scale-dependent metric and causal structures in Quantum Einstein Gravity
• Asymptotic Safety, Emergence and Minimal Length
• Asymptotic safety goes on shell
• RG flow of Weyl-invariant dilaton gravity
• Gravity in $d=2+\epsilon$ dimensions and realizations of the diffeomorphisms group
• Deformed Special Relativity from Asymptotically Safe Gravity
• Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization
• Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
• Some comments on the universal constant in DSR
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• An Extension of Pohlmeyer's Theorem
• Towards Metric-Affine Quantum Gravity