L1/L2 Structural Convergence in Heterotic Compactifications
Year: 2026
Type: preprint
Abstract: This technical note explores a structural-convergence approach to the heterotic string landscape. It separates a structural layer, denoted L1, from a macroscopic or effective realization layer, denoted L2, and examines whether apparently distinct compactifications can be organized before phenomenological selection is imposed. A concrete convergence path is constructed and stress-tested: \[\begin{aligned}10D&\longrightarrow 4D\longrightarrow 6_{\rm int}\longrightarrow \mathbb Z_2\times\mathbb Z_2\\&\longrightarrow 3\ {\rm twisted\ sectors}\longrightarrow 3\times{\bf 16}_{Spin(10)}\\&\longrightarrow SU(4)_C\times SU(2)_L\times SU(2)_R\longrightarrow SU(3)_C\times SU(2)_L\times U(1)_Y .\end{aligned}\] Every transition is classified as established, conditional, or conjectural, and failed selection attempts are retained explicitly. Version 0.2 adds a quantitative GGSO projector test. In a restricted 28-bit projector core, maximal rank of the three 4 × 4 GGSO projector matrices leaves one surviving spinorial state per twisted plane, while equal chirality yields |N_gen| = 3. The same analysis also shows that three-generation selection does not imply vacuum uniqueness. The note further compares large published free-fermionic searches and records a restricted fully moduli-frozen asymmetric heterotic sector in which 10^4 phenomenologically viable GGSO realizations collapse to five distinct partition-function classes. This provides a concrete proof of concept for convergence from a large realization space toward O(1) structural classes. The note does not claim a unique derivation of the Standard Model vacuum. Landscape convergence, N >> 1 → O(1), is explicitly distinguished from the stronger vacuum-uniqueness problem, O(1) → 1. The recurring appearance of the first three even perfect numbers—6, 28, and 496—in ten-dimensional string structures is recorded as a structural motivation, not as evidence of a theorem.
Author: Tanaka, Yasuo
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204236752
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