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    From vortices to instantons on the Euclidean Schwarzschild manifold

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    Date
    2018-01-18
    Authors
    Nagy, Á
    Oliveira, G
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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
    Permalink
    http://hdl.handle.net/10161/16004
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