Quantum scale invariance, cosmological constant and hierarchy problem

TL;DR

The paper proposes quantum-level scale-invariant theories that tolerate spontaneous breaking to produce a massless dilaton, aiming to solve the electroweak hierarchy and cosmological constant problems while preserving standard renormalization-group running at low energies. It introduces field-dependent regularization schemes (SI and GR-SI) to maintain scale invariance in perturbation theory and demonstrates, at one loop in a scalar toy model, that a flat direction can persist, keeping the Higgs mass protected and yielding RG-like running for couplings at accessible energies. Gravity is incorporated compatibly via non-minimal couplings and unimodular gravity, which can enforce a vanishing cosmological constant and generate dynamical dark energy, with the Planck scale emerging from the dilaton vev. The work outlines open questions on nonperturbative validity, renormalizability, and high-energy behavior, while suggesting that SI unimodular gravity could provide a consistent, predictive framework for fundamental physics.

Abstract

We construct a class of theories which are scale invariant on quantum level in all orders of perturbation theory. In a subclass of these models scale invariance is spontaneously broken, leading to the existence of a massless dilaton. The applications of these results to the problem of stability of the electroweak scale against quantum corrections, to the cosmological constant problem and to dark energy are discussed.