Harmonic Higgs Bundles and Coassociative ALE Fibrations

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.

arXiv commentMain 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)

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Cited by in corpus (2)

• T-Branes and $G_2$ Backgrounds
• Deformations of hyperkähler cones