Unifying Gravities with Internal Interactions

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 $SO(10)$.

18 pages, Contribution to "XVI International Workshop LIE THEORY AND ITS APPLICATIONS IN PHYSICS", 16 - 22 June 2025, Varna, Bulgaria