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Instantons on hyperkähler manifolds

Devchand, C., Pontecorvo, M., & Spiro, A. (2020). Instantons on hyperkähler manifolds. Annali di Matematica Pura ed Applicata, 199(2), 533-561. doi:10.1007/s10231-019-00890-5.

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Creators:
Devchand, Chandrashekar1, Author
Pontecorvo, Massimiliano, Author
Spiro, Andrea, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: Mathematics, Differential Geometry, math.DG,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,
Abstract: 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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Dates: 2018-12-162020
Publication Status: Published in print
Pages: 35 pages
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Identifiers: arXiv: 1812.06498
URI: http://arxiv.org/abs/1812.06498
DOI: 10.1007/s10231-019-00890-5
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Title: Annali di Matematica Pura ed Applicata
Source Genre: Journal
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Pages: - Volume / Issue: 199 (2) Sequence Number: - Start / End Page: 533 - 561 Identifier: -