Interacting Multi-Node Conifold Light Sectors

TL;DR

This paper develops a mathematical framework to analyze interacting light sectors in conifold degenerations of Calabi-Yau threefolds, revealing a block structure that isolates coupled conifold light states.

Contribution

It introduces a new multi-node light-sector package with a block-reduced structure theorem, advancing the understanding of conifold degenerations and their Hodge-theoretic properties.

Findings

Global gluing law for corrected extension classes established

Separation of relation collapse and residual interactions demonstrated

Mathematical foundation for multi-node conifold mechanism provided

Abstract

We study finite-node conifold degenerations of Calabi--Yau threefolds from the point of view of interacting light sectors. Although each ordinary double point contributes a rank-one local vanishing sector, the corrected global object need not assemble as a freely independent sum of nodewise pieces. Using the corrected perverse and mixed-Hodge-module degeneration package, the global gluing law for corrected extension classes, and the rigid-flexible atom decomposition on the \(F\)-bundle side, we define an interacting multi-node light-sector package and prove a block-reduced structure theorem. In the block-separated cycle family, the finite-node package separates into two logically distinct layers: relation collapse, controlled by a common relation lattice on the corrected-extension, smoothing, and resolution sides, and residual interaction among the surviving global sectors, controlled by a reduced block interaction matrix on the transport and atom sides. The result isolates the geometric and Hodge-theoretic precursor of coupled conifold light states and provides the mathematical input for a later multi-node reformulation of Strominger's conifold mechanism.