Ricci Flat Metrics, Flat Connections and $G_{2}$-Manifolds

Bobby Samir Acharya; Daniel Andrew Baldwin

Ricci Flat Metrics, Flat Connections and $G_{2}$-Manifolds

High Energy Physics - Theory 2023-12-20 v1 Differential Geometry

Authors: Bobby Samir Acharya , Daniel Andrew Baldwin

Abstract

Inspired by considerations in $M$ -theory, we prove the equivalence between the moduli spaces of (suitably complexified) torsion free $G_{2}$ -structures on 7-manifolds which are families of hyperK\"ahler ALE 4-manifolds fibered over compact flat 3-manifolds $T^{3}/K$ and certain moduli spaces of flat $G^{\mathbb{C}}_{ADE}$ connections on $T^{3}/K$ .

Keywords

Ricci flat metrics flat connections G2-manifolds M-theory moduli spaces torsion free G2-structures hyperKähler ALE manifolds

Cite

@article{arxiv.2312.12311,
  title  = {Ricci Flat Metrics, Flat Connections and $G_{2}$-Manifolds},
  author = {Bobby Samir Acharya and Daniel Andrew Baldwin},
  journal= {arXiv preprint arXiv:2312.12311},
  year   = {2023}
}

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