Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance

TL;DR

This paper explores how Weyl invariant theories can spontaneously generate mass scales through inertial symmetry breaking, maintaining quantum Weyl invariance without scale-invariant regulators, with implications for cosmology and quantum field theory.

Contribution

It introduces a novel mechanism of inertial spontaneous symmetry breaking in Weyl invariant theories, avoiding the need for scale-invariant regulators and clarifying quantum invariance.

Findings

Weyl current structure drives spontaneous symmetry breaking without potentials.

Quantum Weyl invariance can be maintained with appropriate renormalisation conditions.

A Weyl invariant Coleman-Weinberg potential is explicitly computed.

Abstract

Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current, $K_\mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.