Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 1

Almost contact structures on manifolds with a $G_2$ structure

Pages: 143 – 216

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n1.a3

Authors

Xenia de la Ossa (Mathematical Institute, Oxford University, United Kingdom)

Magdalena Larfors (Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden)

Matthew Magill (Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden)

Abstract

We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a $G_2$ structure. These are of interest for certain supersymmetric configurations in string and M‑theory. We compute the torsion of the $SU(3)$ structure associated to an ACMS and apply these computations to heterotic $G_2$ systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.

Published 21 October 2022