G-structures and Superstrings from the Worldsheet

Abstract

$\mathcal{G}$-structures, where $\mathcal{G}$ is a Lie group, are a uniform characterisation of many differential geometric structures of interest in supersymmetric compactifications of string theories. Calabi-Yau $n$-folds are instances of torsion-free $SU(n)$-structures, while more general structures with non-zero torsion are required for heterotic flux compactifications. Exceptional geometries in dimensions $7$ and $8$ with $\mathcal{G}=G_2$ and $Spin(7)$ also feature prominently in this thesis. We discuss multiple connections between such geometries and the worldsheet theory describing strings on them, especially with respect to their chiral symmetry algebras.

PhD thesis. Text overlap with arXiv:1809.06376, arXiv:1809.01138 and arXiv:1710.06865