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.
Highlights
Geometric engineering is at the heart of many applications of string theory, starting with model building for particle physics, the study of superconformal field theories, or sharpening the boundaries of the string theory landscape
A summary of the dictionary between ALE-geometry, i.e. local G2 geometry, the Higgs bundle, Morse-Bott theory on M3 or supersymmetric quantum mechanics (SQM), and the data of the 4d effective theory is provided in table 1. This setup in particular allows modelling the local geometry of M-theory compactifications on twisted connected sum (TCS) G2-manifolds, which have an ALE-fibration over S3
The main result of this paper is a study of the gauge sector of M-theory compactifications on G2-holonomy manifolds to 4d N = 1 supersymmetric gauge theories
Summary
Geometric engineering is at the heart of many applications of string theory, starting with model building for particle physics, the study of superconformal field theories, or sharpening the boundaries of the string theory landscape. This setup in particular allows modelling the local geometry of M-theory compactifications on TCS G2-manifolds, which have an ALE-fibration over S3 (e.g. as in [24]) It will allow us — in the framework of the local Higgs bundle description of the geometry — to make a concrete proposal for the types of deformations and transitions that the geometry needs to undergo. A glossary of our notation and further technical details are relegated to the appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
