Rotationally invariant singular solutions to the Kapustin–Witten equations
- Creators
- He, Siqi
Abstract
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin–Witten equations in 44-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin–Witten equations. The imaginary parts of the solutions are singular. By rescaling, we find some limit behavior for these singular solutions. In addition, for any integer k, we can construct a 5|k| dimensional family of C^1 solutions to the Kapustin–Witten equations on Euclidean space, again with singular imaginary parts. Moreover, we get solutions to the Kapustin–Witten equation with Nahm pole boundary condition over S^3×(0,+∞).
Additional Information
© 2018 International Press. Received 12 March 2016. The author greatly thanks Peter Burton, Anton Kapustin, Edward Witten, Jianfeng Lin, Ciprian Manolescu, Rafe Mazzeo and Yi Ni for their kindness and helpful discussions.Attached Files
Published - MRL-2018-0025-0004-a010.pdf
Submitted - 1510.07706.pdf
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Additional details
- Eprint ID
- 92183
- Resolver ID
- CaltechAUTHORS:20190109-154923635
- Created
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2019-01-10Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field