The heterotic G2 system on contact Calabi--Yau 7-manifolds

We obtain non-trivial solutions to the heterotic G2 system, which are defined on the total spaces of non-trivial circle bundles over Calabi--Yau 3-orbifolds. By adjusting the S1 fibres in proportion to a power of the string constant α′, we obtain a cocalibrated G2-structure the torsion of which realises an arbitrary constant (trivial) dilaton field and an H-flux with nontrivial Chern--Simons defect. We find examples of connections on the tangent bundle and a non-flat G2-instanton induced from the horizontal Calabi--Yau metric which satisfy together the anomaly-free condition, also known as the heterotic Bianchi identity. The connections on the tangent bundle are G2-instantons up to higher order corrections in α′

Flows of G₂-structures on contact Calabi–Yau 7-manifolds

We study the Laplacian flow and coflow on contact Calabi-Yau $7$-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though not eternal and not self-similar) solution of the Laplacian coflow which has an infinite time singularity, that is Type IIb unless the transverse Calabi--Yau geometry is flat. The flows in each case collapse (after normalising the volume) to a lower-dimensional limit, which is either $\mathbb{R}$ for the Laplacian flow or standard $\mathbb{C}^3$ for the Laplacian coflow. We also study the Hitchin flow in this setting, which we show coincides with the Laplacian coflow up to reparametrisation of time, and defines an (incomplete) Calabi--Yau structure on the spacetime track of the flow