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 H1ˇ(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