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arXiv · 1701.03072

Growth of the Higgs field for solutions to the Kapustin-Witten equations on R^4

Clifford Henry Taubes
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Abstract

The Kapustin-Witten equations on R^4 are equations for a pair of connection on the product principle SU(2) bundle and 1-form with values in the product Lie algebra bundle. The 1-form is the Higgs field. A dichotomy is proved to the effect that either the averaged norm of the Higgs field on large radius spheres grows faster than a power of the radius, or its 1-form components everywhere pairwise commute.

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Clifford Henry Taubes. 2017-01-11. Growth of the Higgs field for solutions to the Kapustin-Witten equations on R^4. https://arxiv.org/abs/1701.03072

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