Unification of Conformal and Fuzzy Gravities with Internal Interactions resulting in SO(10) and a Possible Probe through Stochastic Gravitational Wave Background
Gregory Patellis, Danai Roumelioti, Stelios Stefas, George Zoupanos
TL;DR
This paper proposes a gauge-theoretic unification of conformal and fuzzy gravities with internal interactions by gauging an extended tangent group, notably SO(2,16), and explores how spontaneous symmetry breaking can yield Einstein gravity together with SO(10) grand unification that subsequently descends to the Standard Model. It develops the 3D and 4D gravity formulations as gauge theories, constructs conformal and noncommutative (fuzzy) gravity, and demonstrates how Weyl and Majorana fermion conditions can be incorporated to produce realistic chiral fermions in four dimensions. A detailed 1-loop analysis across four breaking channels shows which pathways can satisfy proton-decay bounds and whether cosmic strings could generate a detectable stochastic gravitational-wave background, highlighting the 3221 route as offering potential GW signals while other channels are constrained. The study links high-energy unification with observable cosmological signatures, providing a framework for realizing gravity–gauge unification and guiding experimental tests via GW searches and proton decay experiments.
Abstract
The unification of conformal and fuzzy gravities with internal interactions is based on the facts that i) the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions and ii) both gravitational theories considered here have been formulated in a gauge theoretic way. We review the gauge-theoretic approach of gravities, commenting in particular on their diffeomorphism invariance, and the construction of conformal and noncommutative (fuzzy) gravity using the gauge-theoretic framework. Based on an extension of the four-dimensional tangent group, unification of both gravities with the internal interactions is achieved. Both unified schemes are examined at 1-loop level considering suitable spontaneous symmetry breakings to a SO(10) grand unified theory and consequently down to the Standard Model of particle physics through four specific spontaneous breaking channels. Each channel is examined against proton lifetime experimental bounds and its observation potential through gravitational signal from cosmic strings production is discussed.