Unifying Gravities with Internal Interactions

TL;DR

This paper explores a gauge-theoretic approach to gravity, unifying conformal and noncommutative gravities with internal GUT interactions, emphasizing the role of tangent groups and manifold dimensions.

Contribution

It introduces a unified gauge-theoretic framework for conformal, noncommutative gravities, and GUT-based internal interactions, highlighting the dimension mismatch between tangent groups and manifolds.

Findings

Unified gauge description of different gravity models

Demonstrated compatibility with GUT $SO(10)$

Highlighted the role of tangent group dimensions

Abstract

Reviving the old proposal of describing gravity as a gauge theory first we describe the construction of the Conformal and the Noncommutative (Fuzzy) Gravities in a gauge-theoretic manner. Then stressing the fact that the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions, we show how the above Gravities can be unified with the Internal Interactions, the latter based on the GUT $SO(10)$.