Abstract
We initiate the systematic study of G_2-instantons with SU(2)^2-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on mathbb {R}^4times S^3 with its two explicitly known distinct holonomy G_2 metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We also give an explicit example of sequences of G_2-instantons where “bubbling” and “removable singularity” phenomena occur in the limit.
Highlights
In this article we study G2-instantons: these are examples of Yang–Mills connections on Riemannian manifolds whose holonomy group is contained in the exceptional Lie group G2
The aim of the article is to start the systematic study of SU(2)2-invariant G2-instantons
We summarize the organization of our paper and the main results. Both the BS and BGGG metric have SU(2)2 as a subgroup of their isometry group: SU(2)2 acts with cohomogeneity-1
Summary
In this article we study G2-instantons: these are examples of Yang–Mills connections on Riemannian manifolds whose holonomy group is contained in the exceptional Lie group G2 (so-called G2-manifolds). These connections are, in a sense, analogues of anti-self-dual connections in dimension 4, and are likewise hoped to be used to understand the geometry and topology of G2-manifolds, via the construction of enumerative invariants. As a G2manifold is Ricci flat, for it to admit continuous symmetries it must be noncompact By restricting to this case, we are able to shed light on the still rather poorly understood theory of G2-instantons, in an explicit setting. We can see how general theory works in practice, examine how the ambient geometry affects the G2-instantons and give local models for the behaviour of G2-instantons on compact G2-manifolds
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