Conjecture on the Physical Implications of the Scale Anomaly

TL;DR

The paper links the scale anomaly to the renormalization group and dimensional transmutation, using QCD as the prime example where the strong scale Lambda_QCD emerges from a dimensionless coupling. It then proposes a bold conjecture that all physical mass scales originate from quantum anomalies and that the classical limit is exactly scale invariant, with broad implications for spacetime dimensionality, the cosmological constant, and electroweak dynamics, including dilaton scenarios and Technicolor-like models. The discussion surveys potential realizations in gravity and string theory and emphasizes the prospect of testable dynamical weak-scale frameworks. Overall, it offers a unifying viewpoint that mass and scales arise from quantum effects rather than classical input parameters, inviting further theoretical and experimental exploration.

Abstract

Murray Gell-Mann, after co-inventing QCD, recognized the interplay of the scale anomaly, the renormalization group, and the origin of the strong scale, Lambda_{QCD}. I tell a story, then elaborate this concept, and for the sake of discussion, propose a conjecture that the physical world is scale invariant in the classical, \hbar -> 0, limit. This principle has implications for the dimensionality of space-time, the cosmological constant, the weak scale, and Planck scale.