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Complex monopoles II: The Kapustin--Witten monopole equation

dc.contributor.author Nagy, Akos
dc.contributor.author Oliveira, Gonçalo
dc.date.accessioned 2019-07-02T16:34:00Z
dc.date.available 2019-07-02T16:34:00Z
dc.identifier.uri https://hdl.handle.net/10161/19071
dc.description.abstract We study complexified Bogomolny monopoles in 3 dimensions by complexifying the compact structure groups. In this paper we use the conjugate linear extension of the Hodge star operator which yields a reduction of the Kapustin-Witten equations to 3 dimensions, thus we call its solutions Kapustin-Witten monopoles. Our main result is a vanishing theorem for these monopoles showing that the only finite energy Kapustin-Witten monopoles are the ordinary Bogomolny monopoles. We prove this by analyzing the asymptotic behavior of Kapustin-Witten monopoles, and combining our results with a recent theorem of Taubes.
dc.subject math.DG
dc.subject math.DG
dc.subject 53C07, 58D27, 58E15, 70S15
dc.title Complex monopoles II: The Kapustin--Witten monopole equation
dc.type Journal article
dc.date.updated 2019-07-02T16:34:00Z
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Duke
pubs.organisational-group Mathematics
duke.contributor.orcid Nagy, Akos|0000-0002-1799-7631


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