# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1908.01400