High-Energy Unitarity and Ultraviolet Consistency of the SFT Emergent Vacuum Lattice
Year: 2026
Type: preprint
Abstract: The emergence of macroscopic spacetime geometry from the non-perturbative vacuum of Bosonic String Field Theory (SFT) provides a rigorous microphysical foundation for massive gravity. In this work, we systematically evaluate the high-energy unitarity and ultraviolet (UV) consistency of the emergent linear massive spin-2 field (Fierz-Pauli) dynamically assembled from the primordial crystalline vacuum lattice. While standard massive spin-2 models notoriously suffer from catastrophic UV divergences, strong-coupling issues, and negative-norm states, we demonstrate that the structural rigidity and exact symmetries of the SFT substrate intrinsically shield the macroscopic effective theory from these fatal pathologies. By formally isolating the longitudinal Stückelberg kinematics within the ultraviolet decoupling limit ($\Lambda_3 = (m_g^2 M_{\text{Pl}})^{1/3}$), we prove that the background-shifted BRST cohomology ($\mathcal{Q}_\Psi^2 = 0$) algebraically forces the phononic interactions into strictly divergence-free Galileonic tensor structures. This exact geometric tuning uniquely suppresses higher-order spacetime derivatives, maintaining strictly second-order equations of motion and definitively eradicating the Ostrogradsky instability (the high-energy precursor to the Boulware-Deser ghost). Furthermore, by identifying the longitudinal scalar mode as the exact acoustic Nambu-Goldstone boson of the translation-breaking substrate, we exploit its residual Galilean shift symmetry to establish a rigorous Quantum Non-Renormalization Theorem. We analytically demonstrate that the macroscopic elasticity parameters of the lattice are protected from destructive quantum runaway, as perturbative loop corrections are strictly forbidden from generating generic, un-tuned counterterms. These results conclusively prove that the linear pre-geometric scaffolding derived from SFT remains unconditionally stable, causal, and unitarily sound up to the strong-coupling scale, successfully resolving the UV theoretical impasses of massive gravity and providing a flawless, ghost-free foundation for non-linear macroscopic extensions.
Author: Raso, Domenico
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171402638
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