Higgs Bundles for M-theory on $G_2$-Manifolds
Andreas P. Braun, Sebastjan Cizel, Max Hubner, Sakura Schafer-Nameki
TL;DR
This paper analyzes the gauge sector in M-theory compactifications on $G_2$-manifolds by studying Higgs bundles derived from 7d super Yang-Mills theory, using Morse theory to determine the massless spectrum and exploring chiral matter engineering.
Contribution
It introduces a mathematical framework using Morse and Morse-Bott theory to determine the 4d spectrum from Higgs bundles on $G_2$-manifolds, including TCS examples.
Findings
Derived BPS equations for Higgs bundles on $G_2$-manifolds.
Determined massless spectra for abelian and non-abelian gauge groups.
Provided a method to engineer chiral matter through singular transitions.
Abstract
M-theory compactified on -holonomy manifolds results in 4d 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 . 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) -manifolds, which form the largest class of examples of compact -manifolds. M-theory on TCS -manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of -manifolds and provide a prescription…
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