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Gauge theory in physics and mathematics refers to a field theory whose fields include principal bundles with connection.
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Correspondence between $O(n)$-instantons on $S^4$ and holomorphic bundles over $\mathbb{P}^3$
Theorem 2.9 on page 49 of Atiyah's Geometry of Yang-Mills Fields states that there is a natural correspondence between $U(n)$-instantons on $S^4$ and holomorphic vector bundles of rank $n$ over $\math …