First-Principles Prediction of Material Properties from Topological Invariants

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.