Mass-Dependent Minimal Length and Deformed Quantum Mechanics from Heterotic String Theory

Abstract

A first-principles derivation of deformed quantum mechanics is presented for the alpha '-corrected heterotic string. Upon compactification, the leading corrections induces a quartic momentum correction term to a scalar dispersion relation. This modification is precisely equivalent to a deformed canonical commutator whose single deformation parameter is set by the Calabi-Yau volume, internal curvature, and background fluxes, thereby establishing a finite minimal length. Positivity of the four-derivative coupling confines the Lee-Wick ghost to scales far above the higher-derivative cutoff, whose value and thus the threshold for stringy corrections is fixed by the same geometric data. Moreover, these inputs can amplify the deformation, pushing the minimal length well beyond the string scale. Earlier proposals based on generalized-uncertainty-principle deformations suggested, on purely phenomenological grounds, that quantum-gravity effects might emerge at such elevated scales; the present analysis provides the first rigorous string-theoretic foundation for that scenario. Finally, unlike standard phenomenological models, the deformation derived here depends on the probe mass, yielding significant implications for important physical problems such as species-sensitive black-hole bounds.