Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instantons on hyperk\"ahler manifolds   An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector
bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose
curvature is pointwise invariant under the quaternionic structures of $T_x M, \
x\in M$, 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
$SL_2(\mathbb{C})$-bundle over $M$. Our reformulation affords a streamlined
proof of Uhlenbeck's Compactness Theorem for instantons on
(pseudo-)hyperk\"ahler manifolds.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex