The emergence of macroscopic spacetime geometry from a fundamental quantum framework remains a central challenge in string theory. In this work, we investigate the non-perturbative vacuum structure of Bosonic String Field Theory (SFT) to derive a microscopic foundation for a geometric background. Utilizing Witten's cubic open string action and Wilsonian Effective Field Theory (EFT) techniques, we demonstrate that tachyon condensation mathematically necessitates the formation of a structurally locked, primordial geometric lattice (₋₀ₓₓ₈₂₄) rather than a featureless vacuum. We provide an analytical formulation and robust computational evidence demonstrating the immense effective potential barrier and extreme topological rigidity bounding this crystalline phase. Furthermore, a spectral analysis of the residual fluctuations reveals the exact emergence of a strictly massless vector field, physically trapped on the solitonic defects of the lattice. Exploiting the shifted BRST cohomology, we algebraically prove that this interaction is protected by an exact macroscopic U (1) gauge invariance (Ward-Takahashi identity). Crucially, we demonstrate that the acoustic Nambu-Goldstone phonons of this continuous translation-breaking lattice dynamically act as Stückelberg compensators. These modes physically dress the intrinsic SFT tensor excitations to kinematically assemble a composite, 5-degree-of-freedom macroscopic spin-2 graviton governed by the ghost-free Fierz-Pauli theory. By strictly confining our analysis to the bosonic sector, this framework offers a rigorous, ab initio derivation of a rigid geometric substratum, an emergent gauge connection, and the exact microscopic origins of massive gravity directly from string mechanics, formally establishing the foundation for consistent non-linear geometric EFTs.
Domenico Raso (Thu,) studied this question.