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  Instantons on hyperkähler manifolds

Devchand, C., Pontecorvo, M., & Spiro, A. (in preparation). Instantons on hyperkähler manifolds.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-BB70-D Version Permalink: http://hdl.handle.net/21.11116/0000-0002-E9AA-8
Genre: Paper

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1812.06498.pdf (Preprint), 435KB
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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: 2018-12-16
 Publication Status: Not specified
 Pages: 35 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1812.06498
URI: http://arxiv.org/abs/1812.06498
 Degree: -

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