Harmonic Higgs Bundles and Coassociative ALE Fibrations

TL;DR

This paper constructs a deformation family of G_2-orbifolds with coassociative fibrations, using spectral covers related to Higgs bundles, unifying various approaches in G_2-geometry.

Contribution

It introduces a novel deformation framework for G_2-orbifolds via spectral covers, extending Higgs bundle techniques to G_2-geometry.

Findings

Unified spectral cover framework for coassociative fibrations

Generalization of ADE-fibered Calabi-Yau deformations to G_2-geometry

Construction of deformation families parametrized by sections of fiber bundles

Abstract

Inspired by a string duality, we construct a deformation family for $G_2$-orbifolds given as total spaces of coassociative fibrations by ADE singularities over a closed and oriented smooth three-manifold $Q$. The deformations are parametrized by sections of a fiber bundle on $Q$ that can be interpreted as spectral/cameral covers associated to certain Riemannian analogs of Higgs bundles. The spectral cover picture is a unifying framework for several different approaches to coassociative fibrations appearing in the literature. Our construction generalizes, to the context of $G_2$-geometry, a well-known family of ADE-fibered Calabi-Yau threefolds whose deformations are parametrized by spectral covers of holomorphic Higgs bundles on its base Riemann surface.