A Noncompact Weyl-Einstein-Yang-Mills Model: A Semiclassical Quantum Gravity

TL;DR

This paper develops a perturbatively unitary noncompact Weyl-Einstein-Yang-Mills model in 3+1 dimensions, demonstrating its vacuum structure, symmetry breaking, and particle spectrum, with implications for quantum gravity and gauge theories.

Contribution

It introduces a novel Weyl-invariant gravity model coupled with gauge and Higgs-like fields, analyzing its unitarity, vacuum structure, and symmetry breaking mechanisms.

Findings

Model is unitary in de Sitter and flat vacua.

Spontaneous symmetry breaking generates dimensionful parameters.

The model propagates a massless graviton, scalar bosons, fermions, and vector bosons.

Abstract

We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, $N^2-1$ massless scalar bosons, $N$ massless Dirac fermions, $N^2-1$ Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.