Restrictions of Heterotic G₂ Structures and Instanton Connections

Authors: Xenia de la Ossa, Magdalena Larfors and Eirik E. Svanes

Preprint number: UUITP-31/17

Abstract: This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds Y with a G₂ structure. In particular, such heterotic G₂ systems can be rephrased in terms of a differential Dˇ acting on a complex Ωˇ^∗(Y,Q), where Q=T^∗Y⊕End(TY)⊕End(V) and Dˇ is an appropriate projection of an exterior covariant derivative D which satisfies an instanton condition. The infinitesimal moduli are further parametrised by the first cohomology H¹_Dˇ(Y,Q). We proceed to restrict this system to manifolds X with an SU(3) structure corresponding to supersymmetric compactifications to four dimensional Minkowski space, often referred to as Strominger–Hull solutions. In doing so, we derive a new result: the Strominger–Hull system is equivalent to a particular holomorphic Yang–Mills covariant derivative on Q|_X=T^∗X⊕End(TX)⊕End(V). Arxiv no: https://arxiv.org/abs/1709.06974