Exploratory Draft:Transformational Field Theory Plus: A Renormalisable, Asymptotically-Safe Framework for the Unified Description of Spacetime, Gauge Fields, and Chiral Matter.

Exploratory Draft, TFT+ is a strictly four-dimensional quantum field theory in which a single Lie-algebra–valued master field Ω(x)∈su(5)⋊so(1,3)\Omega(x)\in su(5)\rtimes so(1,3)Ω(x)∈su(5)⋊so(1,3) unifies gauge interactions, gravity, and chiral matter. An emergent Lorentzian metric and an induced Einstein–Hilbert term arise from the (DΩ)2(D\Omega)^2(DΩ)2 sector; the BRST construction removes non-compact ghosts. Exactly three chiral families follow from an Atiyah–Singer index result shifted by a quantised Wess–Zumino inflow; all local and global gauge–gravitational anomalies cancel. The action is power-counting renormalisable; one-loop flows are asymptotically free and two-loop analysis suggests a non-Gaussian UV fixed point (asymptotic safety). A roadmap for FRG and lattice validation is provided, alongside collider/cosmology benchmarks.