Dynamical Topological Massive Gravity: Emergence of Fundamental Interactions from Spacetime TorsionWe propose a geometric unification framework, Dynamical Topological Massive Gravity (DTMG), in which fundamental interactions and matter structures emerge from gravitational dynamics in Einstein-Cartan spacetime with dynamical torsion. The theory is formulated as an effective field framework incorporating both Riemannian curvature and torsion degrees of freedom, where quantum-level torsion induces geometric symmetry breaking without introducing fundamental scalar fields. Torsion-driven spontaneous symmetry breaking leads to an effective separation of interaction sectors through topological and geometric mechanisms. We demonstrate that the trace component of torsion naturally supports an emergent U (1) gauge structure via Kaluza-Klein reduction on compact S¹ × S² topology, while pathways toward chiral SU (2) and color SU (3) structures are identified through torsional defect configurations, though complete non-Abelian gauge derivation remains in progress. Matter and interaction hierarchies arise from topological flux quantization conditions, yielding a dimensionless vacuum parameter V = -6. 73 × 10⁻⁹ without fine-tuning—representing a factor 10⁸ suppression of naive vacuum energy estimates. Topological torsion defects generate mass scales through discrete geometric factors π and 4π linked to four-dimensional Pontryagin indices, reproducing observed quark mass ratios (mₛ/md ≈ 18, mc/mₛ ≈ 12) to within 15%. DTMG yields parameter-free predictions testable within the next decade: Axion mass: 69. 5 ± 8. 2 μeV (ADMX sensitivity: 2025-2028) Mean neutrino mass: = 0. 058 ± 0. 012 eV, implying Σm_ν ≈ 0. 17 ± 0. 04 eV (JUNO/DUNE: 2027-2030) Gravitational wave birefringence: δv/v ~ 10⁻¹⁵ (LIGO O5: 2027+) Modified axion-photon coupling: gₐγγ ~ 10⁻¹¹ GeV⁻¹ (within astrophysical bounds) One-loop renormalizability is verified for the U (1) electromagnetic sector, confirming EFT validity up to the compactification scale Λ ~ 10¹⁵ GeV. Higher-loop corrections and full non-Abelian quantization are deferred to future work. This framework establishes spacetime torsion as a viable geometric mediator linking gravity, gauge structure, and matter generation, providing a concrete, falsifiable pathway toward unification grounded in topological dynamics. Decisive experimental tests will be completed by 2030, offering a rare opportunity for direct verification of geometric unification principles.
Rachaakrit Viriyagul (Fri,) studied this question.