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From vortices to instantons on the Euclidean Schwarzschild manifold

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Date
2018-01-18
Authors
Nagy, Ákos
Oliveira, Gonçalo
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Abstract
The first irreducible solution of the $\SU (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on $\rl^4$ were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on $\rl^4$, the case of the Euclidean Schwarzschild manifold has resisted many efforts for the past 40 years. By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES, we obtain: a complete description of a connected component of the moduli space of unit energy $\SU (2)$ instantons; new examples of instantons with non-integer energy (and non-trivial holonomy at infinity); a complete classification of finite energy, spherically symmetric, $\SU (2)$ instantons. As opposed to the previously known solutions, the generic instanton coming from our construction is not invariant under the full isometry group, in particular not static. Hence disproving a conjecture of Tekin.
Type
Journal article
Subject
math.DG
math.DG
hep-th
math-ph
math.MP
53C07, 58D27, 70S15, 83C57
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https://hdl.handle.net/10161/16004
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Scholars@Duke

Nagy

Akos Nagy

William W. Elliott Assistant Research Professor
I work on elliptic geometric PDE's, mainly coming from low dimensional gauge theories and mathematical physics.
This author no longer has a Scholars@Duke profile, so the information shown here reflects their Duke status at the time this item was deposited.
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