Abstract
An instanton (E, D) on a (pseudo-)hyperkähler manifold M is a vector bundle E associated with a principal G-bundle with a connection D whose curvature is pointwise invariant under the quaternionic structures of T_x M,~xin M, and thus satisfies the Yang–Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on M and equivalence classes of certain holomorphic functions taking values in the Lie algebra of G^{mathbb {C}} defined on an appropriate mathrm {SL}_2({mathbb {C}})-bundle over M. Our reformulation affords a streamlined proof of Uhlenbeck’s compactness theorem for instantons on (pseudo-)hyperkähler manifolds.
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