Quantum scale symmetry

Abstract

Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by quantum fluctuations via the presence of fixed points for running couplings. As for any global symmetry, the ground state or cosmological state may be scale invariant or not. Spontaneous breaking of scale symmetry leads to massive particles and predicts a massless Goldstone boson. A massless particle spectrum follows from scale symmetry of the effective action only if the ground state is scale symmetric. Approximate scale symmetry close to a fixed point leads to important predictions for observations in various areas of fundamental physics.We review consequences of scale symmetry for particle physics, quantum gravity and cosmology. For particle physics, scale symmetry is closely linked to the tiny ratio between the Fermi scale of weak interactions and the Planck scale for gravity. For quantum gravity, scale symmetry is associated to the ultraviolet fixed point which allows for a non-perturbatively renormalizable quantum field theory for all known interactions. The interplay between gravity and particle physics at this fixed point permits to predict couplings of the standard model or other "effective low energy models" for momenta below the Planck mass. In particular, quantum gravity determines the ratio of Higgs boson mass and top quark mass. In cosmology, approximate scale symmetry explains the almost scale-invariant primordial fluctuation spectrum which is at the origin of all structures in the universe. The pseudo-Goldstone boson of spontaneously broken approximate scale symmetry may be responsible for dynamical dark energy and a solution of the cosmological constant problem.

Asymptotic freedom and safety in quantum gravity

“…For A > 0 the quartic scalar couplings become irrelevant parameters. Together with the assumption that the flow of couplings below the Planck scale does not deviate much from the one of the standard model this leads to the successful prediction of the mass of the Higgs boson [87], or more precisely for the mass ratio between top quark and Higgs boson [11,98]. For A > 2 also the scalar mass terms become irrelevant couplings, driving all scalar masses rapidly to zero.…”

“…( 127) have been discussed in Ref. [11]. Instead of a ghost pole on the real axis for q 2 there is a pair of poles in the complex plane.…”

“…See Refs. [4][5][6][7][8][9][10][11][12][13][14][15][16] for reviews. For asymptotic freedom the model is perturbatively renormalizable, while the case of asymptotic safety corresponds to a non-perturbatively renormalizable theory unless all dimensionless couplings at the fixed point are small.…”

Primordial flat frame -- a new view on inflation

“…They are frame-independent and do not depend on χ. In the scaling frame one finds the quantum scale invariant standard model [34][35][36]. The only violation of quantum scale symmetry is then related to the possible presence of an intrinsic mass scale in the dimensionless functions λ(χ) or K(χ).…”

Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

“…Its recent developments are summarized in Refs. [30][31][32][33][34][35][36][37][38][39][40][41][42]. A central object in the functional renormalization group is the effective average action Γ k and its second-order functional derivative Γ (2) k whose inverse form corresponds to the full propagator, so that in general the gauge fixing is required for the gauge field propagator in addition to the ultraviolet (UV) regularization.…”