The heterotic G2 system on contact Calabi--Yau 7-manifolds - Lotay, JD; Earp, HNS (American Mathematical Society, 2023)
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′.