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Higgs bundles for M-theory on G2-manifolds

  • Andreas P. BraunEmail author
  • Sebastjan Cizel
  • Max Hübner
  • Sakura Schäfer-Nameki
Open Access
Regular Article - Theoretical Physics
  • 46 Downloads

Abstract

M-theory compactified on G2-holonomy manifolds results in 4d \( \mathcal{N} \) = 1 supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle M3. We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. The latter generalization allows us to make contact with twisted connected sum (TCS) G2-manifolds, which form the largest class of examples of compact G2-manifolds. M-theory on TCS G2-manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of G2-manifolds and provide a prescription for how to engineer singular transitions to models that have chiral matter in 4d.

Keywords

M-Theory Superstring Vacua Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Andreas P. Braun
    • 1
    Email author
  • Sebastjan Cizel
    • 1
  • Max Hübner
    • 1
  • Sakura Schäfer-Nameki
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUnited Kingdom

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