Grand Unified Theories in Renormalisable, Classically Scale Invariant Gravity

TL;DR

This paper explores how certain gauge theories coupled with scale-invariant gravity can be asymptotically free and undergo dimensional transmutation, leading to a low-energy effective theory with Einstein-Hilbert gravity.

Contribution

It demonstrates the possibility of ultra-violet complete, classically scale-invariant gravity theories with specific gauge groups and scalar content, including the mechanism of symmetry breaking and stability analysis.

Findings

$SO(12)$ theory can be asymptotically free in all couplings.

Dimensional transmutation leads to $SO(12) \to SU(6)\otimes U(1)$ breaking.

Stable minima within ultraviolet fixed points' catchment basin.

Abstract

We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of $SO(12),$ we show that the quantum field theory can be can be asymptotically free in all couplings (hence ultra-violet complete). For a region of parameter space, Dimensional Transmutation occurs, with the adjoint vacuum expectation value breaking $SO(12) \to SU(6)\otimes U(1)$ and producing a Low Energy Effective Theory having Einstein-Hilbert gravity. We verify that certain minima are locally stable and lie within the catchment basin of the ultraviolet fixed points.