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arXiv · 1906.05435

The Kapustin--Witten equations on ALE and ALF gravitational instantons

Ákos Nagy·Gonçalo Oliveira
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Abstract

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 $\mathrm{R}^4$ or $\mathrm{R}^3 \times \mathbb{S}^1$ and the structure group is $\mathrm{SU} (2)$.

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Ákos Nagy, Gonçalo Oliveira. 2019-06-13. The Kapustin--Witten equations on ALE and ALF gravitational instantons. https://doi.org/10.1007/s11005-021-01426-w

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