September 12, 2022
TITLE: Heterotic systems, balanced SU(3)-structures and coclosed G_2-structures in cohomogeneity one manifolds
ABSTRACT: When considering compactifications of heterotic string theory down to 4D, the Hull–Strominger system arises over a six-dimensional manifold endowed with an invariant nowhere-vanishing holomorphic (3,0)-form. When compactifying down to 3D, we get the heterotic G_2 system over a manifold with a G_2-structure. In this talk, we describe these systems and then study the existence of some of the geometric structures required by them in the cohomogeneity one setting.
For the former one, we provide a non-existence result for balanced non-Kähler SU(3)-structures which are invariant under a cohomogeneity one action on a simply connected six-manifold. For the later one, we find a family of coclosed G_2-structures on certain seven-dimensional cohomogeneity one manifolds. Part of this talk is based on a joint work with F. Salvatore.
