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arXiv · 2605.19183

Mass Generation from Embedding Geometry in Surface Nematics

J. A. Santiago·F. Monroy
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Abstract

We show that a nematic field constrained to a curved embedded surface develops an emergent geometric mass in its leading isotropic interaction sector. An auxiliary embedding-space closure mediated by the surface spin connection yields a massive scalar mode \(\chi_n\) with mass set by the extrinsic curvature invariant \(m^2=K_{ab}K^{ab}\). This mass arises directly from embedding geometry, promoting the intrinsic massless nematic interaction into a geometry-controlled massive field. The resulting theory identifies Gaussian curvature as a distributed geometric charge and establishes embedding geometry as the regulator of defect interactions on curved nematic membranes.

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J. A. Santiago, F. Monroy. 2026-05-18. Mass Generation from Embedding Geometry in Surface Nematics. https://arxiv.org/abs/2605.19183

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