Mass Generation from Embedding Geometry in Surface Nematics

TL;DR

This paper demonstrates that embedding geometry induces a mass in nematic fields on curved surfaces, linking curvature to defect interactions and establishing a geometry-controlled massive scalar mode.

Contribution

It introduces a novel mechanism where embedding geometry generates a mass in nematic fields, connecting extrinsic curvature to defect regulation on curved membranes.

Findings

Massive scalar mode hi_n is generated by embedding geometry.

Gaussian curvature acts as a distributed geometric charge.

Embedding geometry regulates defect interactions on nematic membranes.

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.