Harmonic Higgs Bundles and Coassociative ALE Fibrations
Abstract
Inspired by a string duality, we construct a deformation family for -orbifolds given as total spaces of coassociative fibrations by ADE singularities over a closed and oriented smooth three-manifold . The deformations are parametrized by sections of a fiber bundle on 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 -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.
Keywords
Cite
@article{arxiv.1910.10742,
title = {Harmonic Higgs Bundles and Coassociative ALE Fibrations},
author = {Rodrigo Barbosa},
journal= {arXiv preprint arXiv:1910.10742},
year = {2021}
}
Comments
Main Theorem generalized to arbitrary closed orientable smooth three-manifolds. New section added with general construction of ADE-fibered $G_2$-orbifolds. Minor modifications: new subsection on the relation between D-term and the adiabatic limit; new subsections on cameral covers and twistor geometry. Corrected an error in the discussion on character varieties (which did not affect computations)