Unified Curvature Field Theory (UCFT): A Foundational Framework Unifying Gravity, Gauge, and Quantum Structure

In this study, we propose the Unified Curvature Field Theory (UCFT), a framework that captures spacetime, interactions, matter, and quantum properties as unified fluctuations of curvature, grounded in the Principle of Existence: “To exist is to possess curvature.” UCFT is formulated on a 4-dimensional spacetime and is built upon a geometric structure that unifies Riemannian, gauge, and spin connections. A key feature of this theory is that background structures and internal degrees of freedom are not imposed externally, but are intrinsically described as manifestations of curvature dynamics. UCFT is derived from a higher-order theory, the Super Unified Theory (SUT), which encompasses all degrees of freedom via a super-connection. Through dimensional reduction and connection contraction, UCFT emerges naturally from SUT. This paper elucidates the mathematical structure and derivation process of UCFT, and demonstrates how existing frameworks such as string theory and loop quantum gravity can be coherently positioned within the hierarchy of SUT.