📝 SummarXiv

Abstract

Methods for predicting material properties often rely on empirical models or approximations that overlook the fundamental topological nature of quantum interactions. We introduce a topological framework based on string theory and graph geometry that resolves ultraviolet divergences as topological obstructions regularized via Calabi-Yau mappings while preserving symmetries and causal structures, where molecular and condensed matter systems are represented combinatorially through a graph where M-branes form vertices and open strings are twistor-valued edges, holomorphically encoding geometric data from the dynamical system. The resulting effective action is governed by a graph Laplacian whose spectrum dictates stability, excitations, and phase transitions. Applied to uniaxial nematic liquid crystals, the model not only recovers the phenomenological virtual volumes of the Jiron-Castellon model from first principles but also predicts anisotropic thermal expansion coefficients and refractive indices with precision exceeding 0.06\%. The quantitative agreement with experiment, achieved without fitted parameters, demonstrates that principles from quantum gravity and string theory can directly yield accurate predictions for complex materials.