Fundamental Scale Invariance

TL;DR

This paper introduces fundamental scale invariance as a new principle in quantum field theories, offering a scale-free formulation that could explain phenomena like dark energy and provide a UV completion for quantum gravity.

Contribution

It proposes fundamental scale invariance as a novel theoretical principle beyond renormalizability, with implications for particle physics and quantum gravity.

Findings

Scale-invariant formulations admit exact scaling solutions.

Such theories predict properties like a vanishing cosmological constant.

A Yang-Mills based pregeometry is a candidate for quantum gravity.

Abstract

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.