The Kapustin–Witten equations on ALE and ALF gravitational instantons

We study solutions to the Kapustin–Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing theorem in the case when the underlying manifold is R 4 or R 3 ×...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 111; no. 4
Main Authors Nagy, Ákos, Oliveira, Gonçalo
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2021
Springer Nature B.V
Subjects
Complex Systems
Geometry
Group Theory and Generalizations
Instantons
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
70S15
Kapustin–Witten equation
58D27
58E15
Complex monopoles
Gravitational instantons
53C07
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Summary:We study solutions to the Kapustin–Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing theorem in the case when the underlying manifold is R 4 or R 3 × S 1 and the structure group is SU ( 2 ) .
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01426-w